Finite Elements in Analysis and Design最新文献

{"title":"Multi-scale optimization of PC/ABS polymer blends: Microstructural design for superior toughness, strength, and weight efficiency","authors":"A. Francisca Carvalho Alves ,&nbsp;Bernardo P. Ferreira ,&nbsp;F.M. Andrade Pires","doi":"10.1016/j.finel.2025.104407","DOIUrl":"10.1016/j.finel.2025.104407","url":null,"abstract":"<div><div>The PC/ABS polymer blend is widely used in automotive and consumer electronics due to its balanced combination of thermal, mechanical, and processing properties. Its behavior depends on deformation mechanisms such as rubber particle cavitation and debonding at the PC/ABS interface, which vary with loading conditions and morphology. Modeling and optimizing the PC/ABS microstructure is a complex challenge. This work proposes a multi-scale framework to model and optimize different PC/ABS blends, based on: (i) efficient generation of representative volume elements, (ii) accurate constitutive models for the blend phases, and (iii) an unsupervised optimization process for microstructural design. The optimization considers ABS content in the blend, rubber fraction in ABS, and ABS particle orientation to maximize toughness and strength while minimizing cost and weight — a challenging task due to the negative correlation between toughness and strength. To handle the high-dimensional solution space, Multi-Criteria Decision Making techniques are employed to select optimal solutions within the Pareto front. Two case studies are explored: (i) a lightweight, high-toughness application and (ii) a high-strength application. Additionally, the framework is tested in a functionally graded material optimization problem, where a Cook’s membrane is discretized into PC/ABS layers, with the ABS fraction in each layer adjusted to simultaneously minimize maximum displacement and structural weight. The numerical results validate the proposed design framework for PC/ABS while demonstrating its flexibility for other materials and structural applications.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104407"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144633894","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Steady-state and transient thermal stress analysis using a polygonal finite element method","authors":"Yang Yang ,&nbsp;Mingjiao Yan ,&nbsp;Zongliang Zhang ,&nbsp;Dengmiao Hao ,&nbsp;Xuedong Chen ,&nbsp;Weixiong Chen","doi":"10.1016/j.finel.2025.104413","DOIUrl":"10.1016/j.finel.2025.104413","url":null,"abstract":"<div><div>This work presents a polygonal finite element method (PFEM) for the analysis of steady-state and transient thermal stresses in two-dimensional continua. The method employs Wachspress rational basis functions to construct conforming interpolations over arbitrary convex polygonal meshes, providing enhanced geometric flexibility and accuracy in capturing complex boundary conditions and heterogeneous material behavior. A quadtree-based acceleration strategy is introduced to significantly reduce computational cost through the reuse of precomputed stiffness and mass matrices. The PFEM is implemented in ABAQUS via a user-defined element (UEL) framework. Comprehensive benchmark problems, including multi-scale and non-matching mesh scenarios, are conducted to verify the accuracy, convergence properties, and computational efficiency of the method. Results indicate that the PFEM offers notable advantages over conventional FEM in terms of mesh adaptability, solution quality, and runtime performance. The method shows strong potential for large-scale simulations involving thermal–mechanical coupling, complex geometries, and multi-resolution modeling.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104413"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144748731","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Accelerated adaptive phase-field fracture model with an efficient sub-stepping scheme","authors":"Shashank Giri,&nbsp;Akhilesh Rao,&nbsp;Hirshikesh","doi":"10.1016/j.finel.2025.104414","DOIUrl":"10.1016/j.finel.2025.104414","url":null,"abstract":"<div><div>The phase field model emerged as an elegant and powerful computational tool to study fracture behavior and its complex mechanisms in different materials. However, due to the requirement of a fine mesh in areas where fracture occurs, the conventional phase field often demands substantial computational capacity. To overcome this challenge, this work introduces an accelerated adaptive phase-field fracture model that enhances computational efficiency by integrating two key features: (a) adaptive mesh refinement and (b) auto-adaptive sub-stepping algorithms. The adaptive mesh refinement algorithm based on the error indicator derived from the phase-field variable automatically refines the domain where the cracks are likely to propagate. Simultaneously, the auto-sub stepping scheme dynamically adjusts the load increment size during the simulation, which reduces the computational costs while maintaining accuracy and stability. The proposed framework is implemented in FEniCS, an open-source finite element package. The effectiveness and robustness of the proposed implementation are demonstrated through a series of two- and three-dimensional benchmark problems. The results are compared against the standard benchmark problem as well as conventional phase field models that rely on uniform discretization and manual time-step increments.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104414"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144766966","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"High-resolution thermal simulation framework for extrusion-based additive manufacturing of complex geometries","authors":"Dhruv Gamdha,&nbsp;Kumar Saurabh,&nbsp;Baskar Ganapathysubramanian,&nbsp;Adarsh Krishnamurthy","doi":"10.1016/j.finel.2025.104410","DOIUrl":"10.1016/j.finel.2025.104410","url":null,"abstract":"<div><div>Accurate simulation of the printing process is essential for improving print quality, reducing waste, and optimizing the printing parameters of extrusion-based additive manufacturing. Traditional additive manufacturing simulations are very compute-intensive and are not scalable to simulate even moderately sized geometries. In this paper, we propose a general framework for creating a digital twin of the dynamic printing process by performing physics simulations with the intermediate print geometries. Our framework takes a general extrusion-based additive manufacturing G-code, generates an analysis-suitable voxelized geometry representation from the print schedule, and performs physics-based (transient thermal) simulations of the printing process. Our approach leverages adaptive octree meshes for both geometry representation as well as for fast simulations to address real-time predictions. We demonstrate the effectiveness of our method by simulating the printing of complex geometries at high voxel resolutions with both sparse and dense infills. Our results show that this approach scales to high voxel resolutions and can predict the transient heat distribution as the print progresses. Because the simulation runs faster than real print time, the same engine could, in principle, feed thermal predictions back to the machine controller (e.g., to adjust fan speed or extrusion rate). The present study establishes the computational foundations for a real-time <em>digital twin</em>, which can be used for closed control loop control in the future.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104410"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144831165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A novel class of Hessian recovery-based numerical methods for solving biharmonic equations and their applications in phase field modeling","authors":"Minqiang Xu ,&nbsp;Lei Zhang ,&nbsp;Boying Wu ,&nbsp;Kai Liu","doi":"10.1016/j.finel.2025.104405","DOIUrl":"10.1016/j.finel.2025.104405","url":null,"abstract":"<div><div>In this paper, we introduce unified Hessian recovery-based <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> finite element methods (HRB–FEM) and finite volume methods (HRB–FVM) for 2D biharmonic equations. Within the framework of Petrov–Galerkin methods, we propose a novel <span><math><mrow><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup><mo>−</mo><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></mrow></math></span> formulation. Initially, we employ the Hessian recovery operator to discretize the Laplacian operator, subsequently integrating it into both the standard <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span> Lagrange finite element framework and finite volume framework. Through tailored treatments of Neumann-type boundary conditions aimed at reducing computational overhead, we extend our Hessian recovery-based FEM to address phase field equations. Numerical experiments confirm optimal order of convergence under <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> and <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span> norms, demonstrating rates of <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>k</mi><mo>+</mo><mn>1</mn></mrow></msup><mo>)</mo></mrow></mrow></math></span> and <span><math><mrow><mi>O</mi><mrow><mo>(</mo><msup><mrow><mi>h</mi></mrow><mrow><mi>k</mi></mrow></msup><mo>)</mo></mrow></mrow></math></span> respectively for both proposed methods. Furthermore, a series of benchmark tests highlight the robustness of our approach and its ability to faithfully capture the physical characteristics during prolonged simulations of phase field equations.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104405"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144614377","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Integration of hierarchical quadrature element method with a minimum-increment remeshing strategy for simulating coupled thermo-mechanical fracture in quasi-brittle materials","authors":"Sihua Hu ,&nbsp;Xing Luo ,&nbsp;Wei Xiang","doi":"10.1016/j.finel.2025.104434","DOIUrl":"10.1016/j.finel.2025.104434","url":null,"abstract":"<div><div>This paper presents a <em>p</em>-version finite element framework for analyzing the thermal fracture behavior of quasi-brittle materials under coupled thermo-mechanical loadings. The proposed formulation, based on the hierarchical quadrature element method (HQEM), enables accurate capture of temperature gradients even on relatively coarse meshes. Its accuracy in simulating heat conduction and thermally induced deformation is validated against ABAQUS results.</div><div>The HQEM is integrated with the virtual crack closure method to compute fracture parameters under combined thermal and mechanical loadings, significantly reducing mesh refinement and preprocessing effort compared to conventional <em>h</em>-version FEM. To efficiently track complex crack paths, a minimum-increment remeshing strategy is introduced, which controls element growth while preserving the geometric accuracy of crack paths during iterative crack propagation analysis, significantly reducing the computational cost associated with frequent remeshing. Applications to four representative numerical examples demonstrate excellent agreement with existing literature, confirming the reliability and accuracy of the proposed approach for coupled thermo-mechanical fracture analysis.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104434"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144861159","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Cheap and stable quadrature on polyhedral elements","authors":"Alvise Sommariva,&nbsp;Marco Vianello","doi":"10.1016/j.finel.2025.104409","DOIUrl":"10.1016/j.finel.2025.104409","url":null,"abstract":"<div><div>We discuss a cheap tetrahedra-free approach to the numerical integration of polynomials on polyhedral elements, based on hyperinterpolation in a bounding box and Chebyshev moment computation via the divergence theorem. No conditioning issues arise, since no matrix factorization or inversion is needed. The resulting quadrature formula is theoretically stable even in the presence of some negative weights.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104409"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144664703","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A thermodynamically based explicit transient dynamics framework for large transformation contact problems","authors":"Paul Larousse ,&nbsp;David Dureisseix ,&nbsp;Anthony Gravouil ,&nbsp;Jean Di Stasio","doi":"10.1016/j.finel.2025.104411","DOIUrl":"10.1016/j.finel.2025.104411","url":null,"abstract":"<div><div>An explicit framework to solve fast dynamic problems with large transformation and rigid-deformable contact, involving non-regular and non-linear behaviors is under concern. Based on previous works, a framework combining thermodynamically-based behaviors and the so-called explicit symplectic time integrator CD-Lagrange owning good energy properties is developed. In this article, the interface behavior is modeled with a cohesive zone model, the RCCM delayed damage model, and for the deformable body, a hyper-elastic Saint-Venant–Kirchhoff model coupled with viscous effects is chosen. The modular proposed framework shows that switching between a large transformation or a small perturbation problem (and a wide range of non-linear laws both on the interface or in the bulk) is non-intrusive in terms of numerical implementation and dedicated spatial interface integration in the framework of finite elements. In this work, illustrations and feasibility are exemplified for a simplified unmolding industrial case.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104411"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144680254","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"An experimental and numerical dynamic study of thick sandwich beams using a mixed {3,2}-RZT formulation","authors":"Matteo Sorrenti,&nbsp;Marco Gherlone","doi":"10.1016/j.finel.2025.104435","DOIUrl":"10.1016/j.finel.2025.104435","url":null,"abstract":"&lt;div&gt;&lt;div&gt;This work presents some numerical and experimental validations of the free-vibration behaviour of thick sandwich beams using the mixed {3,2}-Refined Zigzag Theory (&lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mtext&gt;RZT&lt;/mtext&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt;). The &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mtext&gt;RZT&lt;/mtext&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; formulation enhances the Timoshenko's kinematics with a piece-wise zigzag cubic distribution of the axial displacement, and a smoothed parabolic variation for the transverse deflection. Simultaneously, an a-priori assumption is made for the transverse normal stress and the transverse shear one: the former is assumed to be a third-order power series expansion of the thickness coordinate, while the latter is derived through the integration of Cauchy's equations. The equations of motion and consistent boundary conditions for the free-vibration problem are derived through the Hellinger-Reissner (HR) theorem. Taking advantage of the C&lt;sup&gt;0&lt;/sup&gt;-continuity requirement in the mixed governing functional, a simple two-node beam finite element (FE) is formulated, i.e., the &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msubsup&gt;&lt;mtext&gt;RZT&lt;/mtext&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; element. The analytical and FE performances of the proposed &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mtext&gt;RZT&lt;/mtext&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; model are first addressed by means of a comparison with high-fidelity 3D FE models. Subsequently, an experimental campaign is conducted using LASER Doppler Vibrometry (LDV) to evaluate the modal parameters of a series of thick sandwich beams made of aluminium alloy face-sheets and Rohacell® WF110 core. The experimental results concerning the natural frequencies and modal shapes of the thick sandwich beam specimens under free-free boundary conditions are compared with those given by &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;msubsup&gt;&lt;mtext&gt;RZT&lt;/mtext&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span&gt; and high-fidelity 3D FE models. The numerical-experimental assessment highlights the effect of core and face-sheet thickness on frequency estimations, as well as the complexity of reproducing in the numerical model the experimental uncertainties. In general, the &lt;span&gt;&lt;math&gt;&lt;mrow&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;mi&gt;B&lt;/mi&gt;&lt;mo&gt;−&lt;/mo&gt;&lt;msubsup&gt;&lt;mtext&gt;RZT&lt;/mtext&gt;&lt;mrow&gt;&lt;mo&gt;{&lt;/mo&gt;&lt;mrow&gt;&lt;mn&gt;3&lt;/mn&gt;&lt;mo&gt;,&lt;/mo&gt;&lt;mn&gt;2&lt;/mn&gt;&lt;/mrow&gt;&lt;mo&gt;}&lt;/mo&gt;&lt;/mrow&gt;&lt;mrow&gt;&lt;mo&gt;(&lt;/mo&gt;&lt;mi&gt;m&lt;/mi&gt;&lt;mo&gt;)&lt;/mo&gt;&lt;/mrow&gt;&lt;/msubsup&gt;&lt;/mrow&gt;&lt;/math&gt;&lt;/span","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104435"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144885420","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Two stabilized finite element methods based on local polynomial pressure projection for the steady-state Navier–Stokes–Darcy problem","authors":"Liyun Zuo ,&nbsp;Guangzhi Du","doi":"10.1016/j.finel.2025.104420","DOIUrl":"10.1016/j.finel.2025.104420","url":null,"abstract":"<div><div>This study presents two stabilized finite element methods based on local polynomial pressure projections for the mixed steady-state Navier–Stokes–Darcy problem by utilizing the equal order finite element pairs, the <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-<span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span>-<span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>1</mn></mrow></msub></math></span> and <span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-<span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span>-<span><math><msub><mrow><mi>P</mi></mrow><mrow><mn>2</mn></mrow></msub></math></span> element pairs, for approximating the fluid velocity, kinematic pressure and dynamic pressure, respectively. The presented stabilized methods possess many chief characteristics, for instance, parameter free, simple calculation, element level implementation. The optimal error estimates are established. Finally, some comprehensively numerical tests are reported to examine the efficiency and robustness of the proposed algorithms.</div></div>","PeriodicalId":56133,"journal":{"name":"Finite Elements in Analysis and Design","volume":"251 ","pages":"Article 104420"},"PeriodicalIF":3.5,"publicationDate":"2025-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"144841668","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}