Computers & Mathematics with Applications最新文献

{"title":"Mixed virtual element methods for the poro-elastodynamics model on polygonal grids","authors":"Yanli Chen ,&nbsp;Xin Liu ,&nbsp;Wenhui Zhang ,&nbsp;Yufeng Nie","doi":"10.1016/j.camwa.2024.09.025","DOIUrl":"10.1016/j.camwa.2024.09.025","url":null,"abstract":"<div><div>This work introduces and analyzes the mixed virtual element method on polygonal meshes for the numerical discretization of poro-elastodynamics models. For spatial discretization, we employ the mixed virtual element method on polygonal meshes, coupled with Newmark-<em>β</em> integration schemes for time discretization. We present a stability analysis for both the continuous and semi-discrete problems and derive error estimates for the energy norm in the semi-discrete case. Numerical experiments are conducted to verify the theoretical analysis, and the results on Voronoi meshes demonstrate that the algorithm effectively handles various dynamic viscosities.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"174 ","pages":"Pages 431-448"},"PeriodicalIF":2.9,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421915","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Theoretical analysis and numerical scheme of local conservative characteristic finite difference for 2-d advection diffusion equations","authors":"Yiyang Wang,&nbsp;Zhongguo Zhou","doi":"10.1016/j.camwa.2024.09.032","DOIUrl":"10.1016/j.camwa.2024.09.032","url":null,"abstract":"<div><div>In this paper, the mass conservative characteristic finite difference scheme for 2-d advection diffusion equations is analyzed. Firstly, along <em>x</em>-direction, we obtain the solutions <span><math><mo>{</mo><msubsup><mrow><mover><mrow><mi>U</mi></mrow><mrow><mo>˜</mo></mrow></mover></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow><mrow><mi>n</mi></mrow></msubsup><mo>}</mo></math></span> by applying the piecewise parabolic method (PPM) on the Lagrangian grid where <span><math><mover><mrow><mi>x</mi></mrow><mrow><mo>¯</mo></mrow></mover></math></span> is solved using the first-order Runge Kutta scheme. Secondly, the mass <span><math><msubsup><mrow><mover><mrow><mi>M</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow><mrow><mi>n</mi></mrow></msubsup></math></span> over <span><math><msub><mrow><mover><mrow><mi>Ω</mi></mrow><mrow><mo>¯</mo></mrow></mover></mrow><mrow><mi>i</mi><mo>,</mo><mi>j</mi></mrow></msub><mo>(</mo><msup><mrow><mi>t</mi></mrow><mrow><mi>n</mi></mrow></msup><mo>)</mo></math></span> are solved by the PPM scheme along <em>y</em>-direction. Finally, the local conservative characteristic finite difference scheme is constructed. By some auxiliary lemmas, we prove our scheme is stable and obtain the optimal error estimate. Our scheme is proved to be of second order convergence in space and of first order in time. Numerical experiments are used to verify the theoretical analysis.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"175 ","pages":"Pages 255-275"},"PeriodicalIF":2.9,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Elastic bending total variation model for image inpainting with operator splitting method","authors":"Caixia Nan ,&nbsp;Qian Zhang","doi":"10.1016/j.camwa.2024.09.023","DOIUrl":"10.1016/j.camwa.2024.09.023","url":null,"abstract":"<div><div>The elastic bending energy model is commonly used to describe the shape transformation of biological lipid vesicles, making it a classical phase field model. In this paper, by coupling the elastic bending energy with the total variation (TV) regularization, we develop an elastic bending-TV model for image inpainting. By solving the energy minimization problem of this model, we obtain the results for image processing. We adopt an operator splitting method for the model and the numerical scheme involves the introduction of two vector- and scalar-valued functions to reconstruct this functional. The energy minimization problem is transformed into finding the steady state solution of artificial time-dependent PDE systems. At each fractional step, we can find either a closed-form solution or being solved by an efficient algorithm, which is a very robust and stable algorithm. Experimental results validate the superiority of our model and the effectiveness of the scheme for image inpainting.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"176 ","pages":"Pages 150-164"},"PeriodicalIF":2.9,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421297","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A posteriori error estimates of Darcy flows with Robin-type jump interface conditions","authors":"Jeonghun J. Lee","doi":"10.1016/j.camwa.2024.09.031","DOIUrl":"10.1016/j.camwa.2024.09.031","url":null,"abstract":"<div><div>In this work we develop an a posteriori error estimator for mixed finite element methods of Darcy flow problems with Robin-type jump interface conditions. We construct an energy-norm type a posteriori error estimator using the Stenberg post-processing. The reliability of the estimator is proved using an interface-adapted Helmholtz-type decomposition and an interface-adapted Scott–Zhang type interpolation operator. A local efficiency and the reliability of post-processed pressure are also proved. Numerical results illustrating adaptivity algorithms using our estimator are included.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"174 ","pages":"Pages 417-430"},"PeriodicalIF":2.9,"publicationDate":"2024-10-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421914","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Isogeometric analysis of the Laplace eigenvalue problem on circular sectors: Regularity properties and graded meshes","authors":"Thomas Apel,&nbsp;Philipp Zilk","doi":"10.1016/j.camwa.2024.09.018","DOIUrl":"10.1016/j.camwa.2024.09.018","url":null,"abstract":"<div><div>The Laplace eigenvalue problem on circular sectors has eigenfunctions with corner singularities. Standard methods may produce suboptimal approximation results. To address this issue, a novel numerical algorithm that enhances standard isogeometric analysis is proposed in this paper by using a single-patch graded mesh refinement scheme. Numerical tests demonstrate optimal convergence rates for both the eigenvalues and eigenfunctions. Furthermore, the results show that smooth splines possess a superior approximation constant compared to their <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>0</mn></mrow></msup></math></span>-continuous counterparts for the lower part of the Laplace spectrum. This is an extension of previous findings about excellent spectral approximation properties of smooth splines on rectangular domains to circular sectors. In addition, graded meshes prove to be particularly advantageous for an accurate approximation of a limited number of eigenvalues. Finally, a hierarchical mesh structure is presented to avoid anisotropic elements in the physical domain and to omit redundant degrees of freedom in the vicinity of the singularity. Numerical results validate the effectiveness of hierarchical mesh grading for simulating eigenfunctions of low and high regularity.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"175 ","pages":"Pages 236-254"},"PeriodicalIF":2.9,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142419166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Two novel linearized energy-conserving finite element schemes for nonlinear regularized long wave equation","authors":"Lele Wang,&nbsp;Xin Liao,&nbsp;Can Chen","doi":"10.1016/j.camwa.2024.09.030","DOIUrl":"10.1016/j.camwa.2024.09.030","url":null,"abstract":"<div><div>In this paper, two linearized second-order energy-conserving schemes for the nonlinear regularized long wave (RLW) equation are introduced, the unconditional superclose and superconvergence results are presented by using the conforming finite element method (FEM). Initially, through a skillful decomposition of the nonlinear term, two linearized second-order fully discrete schemes are developed. Compared to the previous nonlinear approaches, these schemes significantly reduce the number of iterations and improve computational efficiency; moreover, they conserve energy, and ensure the boundedness of the numerical solution in the <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-norm directly, which represents an advancement over the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup></math></span>-norm boundedness reported in prior studies. Secondly, based on the boundedness of the FE solution, the Ritz projection operator and high-precision results of the linear triangular element, the error estimates for superclose and superconvergence are derived without any restrictions on the ratio between time step size Δ<em>t</em> and spatial mesh size <em>h</em>. Finally, four numerical examples are provided to confirm the accuracy of the theoretical analysis and the effectiveness of the method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"174 ","pages":"Pages 361-378"},"PeriodicalIF":2.9,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Reweighted Nadaraya–Watson estimation of stochastic volatility jump-diffusion models","authors":"Shaolin Ji,&nbsp;Linlin Zhu","doi":"10.1016/j.camwa.2024.09.029","DOIUrl":"10.1016/j.camwa.2024.09.029","url":null,"abstract":"<div><div>In this paper, we construct the reweighted Nadaraya–Watson estimators of the infinitesimal moments for the volatility process of the stochastic volatility models, with the application of the threshold estimator of the unobserved volatility process. Our model includes jumps in both the underlying asset price and its volatility process. We derive the asymptotic properties of the estimators under the infill and long span assumptions. The results are useful for identification of the process. The finite-sample performance of the estimators is studied through Monte Carlo simulation.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"174 ","pages":"Pages 352-360"},"PeriodicalIF":2.9,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421788","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Acoustic and soliton propagation using fully-discrete energy preserving partially implicit scheme in homogeneous and heterogeneous mediums","authors":"Jyoti Jaglan ,&nbsp;Vikas Maurya ,&nbsp;Ankit Singh ,&nbsp;Vivek S. Yadav ,&nbsp;Manoj K. Rajpoot","doi":"10.1016/j.camwa.2024.09.033","DOIUrl":"10.1016/j.camwa.2024.09.033","url":null,"abstract":"<div><div>This study presents an energy preserving partially implicit scheme for the simulation of wave propagation in homogeneous and heterogeneous mediums. Despite its implicit nature, the developed scheme does not require any explicit numerical or analytical inversion of the coefficient matrix. Theoretical analysis and numerical experiments are performed to validate the energy preserving properties of the fully-discrete scheme. Convergence analysis is also performed to assess the rate of convergence of the developed scheme. The efficiency and accuracy of the developed scheme are validated by numerical solutions of wave propagation in layered heterogeneous mediums. Furthermore, simulations of soliton propagation following nonlinear sine-Gordon and Klein-Gordon equations in homogeneous and heterogeneous mediums are discussed. Numerical solutions are also compared with the results available in the literature. The present method accurately resolves the physical characteristics of the chosen problems, competing well with existing multi-stage time-integration methods. Moreover, it has significantly lower computational complexity than the four-stage, fourth-order Runge-Kutta-Nyström method.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"174 ","pages":"Pages 379-396"},"PeriodicalIF":2.9,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421819","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The influence of parasitic modes on stable lattice Boltzmann schemes and weakly unstable multi-step Finite Difference schemes","authors":"Thomas Bellotti","doi":"10.1016/j.camwa.2024.09.028","DOIUrl":"10.1016/j.camwa.2024.09.028","url":null,"abstract":"<div><div>Numerical analysis for linear constant-coefficient multi-step Finite Difference schemes is a longstanding topic, developed approximately fifty years ago. It relies on the stability of the scheme, and thus—within the <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span> setting—on the absence of multiple roots of the amplification polynomial on the unit circle. This allows for the decoupling, while discussing the convergence of the method, of the study of the consistency of the scheme from the precise knowledge of its parasitic/spurious modes, so that the methods can be essentially studied as if they had only one step. Furthermore, stability alleviates the need to delve into the complexities of floating-point arithmetic on computers, which can be challenging topics to address. In this paper, we demonstrate that in the case of “weakly” unstable Finite Difference schemes with multiple roots on the unit circle, although the schemes may remain stable, considering parasitic modes is essential in studying their consistency and, consequently, their convergence. This research was prompted by unexpected numerical results on stable lattice Boltzmann schemes, which can be rewritten in terms of multi-step Finite Difference schemes. Unlike Finite Difference schemes, rigorous numerical analysis for lattice Boltzmann schemes is a contemporary topic with much left for future discoveries. Initial expectations suggested that third-order initialization schemes would suffice to maintain the accuracy of fourth-order schemes. However, this assumption proved incorrect for weakly unstable Finite Difference schemes and for stable lattice Boltzmann methods. This borderline scenario underscores that particular care must be adopted for lattice Boltzmann schemes, and the significance of genuine stability in facilitating the construction of Lax-Richtmyer-like theorems and in mastering the impact of round-off errors concerning Finite Difference schemes. Despite the simplicity and apparent lack of practical usage of the linear transport equation at constant velocity considered throughout the paper, we demonstrate that high-order lattice Boltzmann schemes for this equation can be used to tackle nonlinear systems of conservation laws relying on a <em>Jin-Xin</em> approximation and high-order splitting formulæ.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"174 ","pages":"Pages 397-416"},"PeriodicalIF":2.9,"publicationDate":"2024-10-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421913","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Control of a nonlinear wave equation with a dynamic boundary condition","authors":"Rodrigo L.R. Madureira ,&nbsp;Mauro A. Rincon ,&nbsp;Ricardo F. Apolaya ,&nbsp;Bruno A. Carmo","doi":"10.1016/j.camwa.2024.09.034","DOIUrl":"10.1016/j.camwa.2024.09.034","url":null,"abstract":"<div><div>Existence, uniqueness, energy decay, and approximate numerical solution for the nonlinear wave equation with dynamic control at the boundary is being studied in this work. The theoretical analysis of the problem will be conducted using the Faedo-Galerkin method and compactness results. To obtain the approximate numerical solution, a combined approach of the finite element method and a finite difference method will be employed, known as the linearized Crank-Nicolson Galerkin method. This method optimizes the calculations and preserves the quadratic order of convergence in time. Finally, numerical experiments are performed, and tables and graphs are presented to illustrate the theoretical convergence rates and demonstrate the consistency between theoretical and numerical results.</div></div>","PeriodicalId":55218,"journal":{"name":"Computers & Mathematics with Applications","volume":"176 ","pages":"Pages 140-149"},"PeriodicalIF":2.9,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142421296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}