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Efficient numerical methods to approach solutions of quasi-static contact problems
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100535
Lionel Ouya Ndjansi, Laurent Tchoualag, Jean Louis Woukeng
{"title":"Efficient numerical methods to approach solutions of quasi-static contact problems","authors":"Lionel Ouya Ndjansi,&nbsp;Laurent Tchoualag,&nbsp;Jean Louis Woukeng","doi":"10.1016/j.rinam.2024.100535","DOIUrl":"10.1016/j.rinam.2024.100535","url":null,"abstract":"<div><div>In this paper, a new boundary element method and generalized Newton method for the resolution of quasi-static contact problems with friction in 2D is presented. The time discretization of the model and the mixed duality-fixed point formulation combined with augmented lagrangian approach are considered. This leads at each time step, to a system of static contact problem with Coulomb friction, where the study is carried out by the dual–primal active set method. After proving the well-posedness of the regularized dual problem and convergence to the solutions of the static problem, the generalized Newton method based on active set strategy method and fixed point method are constructed. An error estimate for the Galerkin discretization is established and some numerical examples are presented.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100535"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098510","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Stochastic differential equations harvesting optimization with stochastic prices: Formulation and numerical solution
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100533
Miguel Reis, Nuno M. Brites
{"title":"Stochastic differential equations harvesting optimization with stochastic prices: Formulation and numerical solution","authors":"Miguel Reis,&nbsp;Nuno M. Brites","doi":"10.1016/j.rinam.2024.100533","DOIUrl":"10.1016/j.rinam.2024.100533","url":null,"abstract":"<div><div>This work aims to achieve optimal harvesting in a random setting with a stochastic price structure. We use a general growth function to model the harvested population, a geometric Brownian motion to model price change, and add fluctuations in the interest rate over time to complete the analysis. Following this, we make use of the stochastic dynamic programming technique in order to obtain the Hamilton–Jacobi–Bellman equation, which ultimately results in the optimal combination of profit and effort. We employ the Crank–Nicolson discretization approach to obtain a numerical solution to the Hamilton–Jacobi–Bellman partial differential equation. For application purposes, we consider a Gompertz growth model and realistic data based on the Bangladesh shrimp.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100533"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143150063","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A finite element/polynomial spectral mixed approximation for the Stokes problem
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2025.100550
Shinya Uchiumi
{"title":"A finite element/polynomial spectral mixed approximation for the Stokes problem","authors":"Shinya Uchiumi","doi":"10.1016/j.rinam.2025.100550","DOIUrl":"10.1016/j.rinam.2025.100550","url":null,"abstract":"<div><div>A mixed Galerkin approximation for the Stokes problem is proposed. The finite element approximation is used for the velocity and the polynomial spectral approximation for pressure. The numerical results show that the proposed method has higher accuracy for a problem with a large external force, and efficiency in solving the resultant linear system using an iterative solver.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100550"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143487225","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Kolmogorov bounds for drift parameter estimation of continuously-observed SPDEs
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2025.100538
Fares Alazemi, Abdulaziz Alsenafi, Khalifa Es-Sebaiy
{"title":"Kolmogorov bounds for drift parameter estimation of continuously-observed SPDEs","authors":"Fares Alazemi,&nbsp;Abdulaziz Alsenafi,&nbsp;Khalifa Es-Sebaiy","doi":"10.1016/j.rinam.2025.100538","DOIUrl":"10.1016/j.rinam.2025.100538","url":null,"abstract":"<div><div>The purpose of this paper is to study the asymptotic behavior of the maximum likelihood estimator (MLE) and the minimum contrast estimator (MCE) of the drift coefficient for a stochastic partial differential equation based on continuous time observations of the Fourier coefficients <span><math><mrow><msub><mrow><mi>u</mi></mrow><mrow><mi>k</mi></mrow></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>,</mo><mspace></mspace><mi>k</mi><mo>=</mo><mn>1</mn><mo>,</mo><mo>…</mo><mo>,</mo><mi>N</mi></mrow></math></span> of the solution, over some finite interval of time <span><math><mrow><mo>[</mo><mn>0</mn><mo>,</mo><mi>T</mi><mo>]</mo></mrow></math></span>. More precisely, we derive Berry–Esseen bounds in Kolmogorov distance for the MLE and MCE when <span><math><mrow><mi>N</mi><mo>→</mo><mi>∞</mi></mrow></math></span> and/or <span><math><mrow><mi>T</mi><mo>→</mo><mi>∞</mi></mrow></math></span>. Moreover, we prove the strong consistency of the MCE as <span><math><mrow><mi>N</mi><mo>→</mo><mi>∞</mi></mrow></math></span> and/or <span><math><mrow><mi>T</mi><mo>→</mo><mi>∞</mi></mrow></math></span>.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100538"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143149996","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Fully decoupled SAV Fourier-spectral scheme for the Cahn–Hilliard–Hele–Shaw system
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100534
Linhui Zhang , Hongen Jia , Hongbin Wang
{"title":"Fully decoupled SAV Fourier-spectral scheme for the Cahn–Hilliard–Hele–Shaw system","authors":"Linhui Zhang ,&nbsp;Hongen Jia ,&nbsp;Hongbin Wang","doi":"10.1016/j.rinam.2024.100534","DOIUrl":"10.1016/j.rinam.2024.100534","url":null,"abstract":"<div><div>In this paper, we construct first- and second-order fully discrete schemes for the Cahn–Hilliard–Hele–Shaw system based on the Fourier-spectral method for spatial discretization. For temporal discretization, we combine two efficient approaches, including the scalar auxiliary variable (SAV) method for linearizing nonlinear potentials and the zero-energy-contribution method (ZEC) for decoupling nonlinear couplings. These schemes are linear, fully decoupled, and unconditionally energy stable, requiring only the solution of a sequence of elliptic equations with constant coefficients at each time step. The rigorous proof of the error analysis for the first-order scheme is shown. In addition, several numerical examples are presented to demonstrate the stability, accuracy, and efficiency of the proposed scheme.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100534"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143149997","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A novel n-L1 image restoration approach
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100521
Lufeng Bai
{"title":"A novel n-L1 image restoration approach","authors":"Lufeng Bai","doi":"10.1016/j.rinam.2024.100521","DOIUrl":"10.1016/j.rinam.2024.100521","url":null,"abstract":"<div><div>This article presents a variational image restoration model and an accelerated algorithm to recover a clear image from a noisy and blurred version. The model involves solving a high-order nonlinear partial differential equation, which can be computationally expensive. This paper proposes the use of the accelerated alternating direction method of multipliers (ADMM) to solve a constrained minimization problem. The method is based on a variable splitting scheme and an augmented Lagrangian method, resulting in a fast and convergent algorithm. The paper presents a convergence analysis of the proposed algorithm under certain conditions. Numerical results and comparisons demonstrate that our model and algorithm outperform some state-of-the-art algorithms for image restoration in terms of computational time.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100521"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098503","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Two-grid mixed finite element method combined with the BDF2-θ for a two-dimensional nonlinear fractional pseudo-hyperbolic wave equation
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100530
Yan Wang, Yining Yang, Nian Wang, Hong Li, Yang Liu
{"title":"Two-grid mixed finite element method combined with the BDF2-θ for a two-dimensional nonlinear fractional pseudo-hyperbolic wave equation","authors":"Yan Wang,&nbsp;Yining Yang,&nbsp;Nian Wang,&nbsp;Hong Li,&nbsp;Yang Liu","doi":"10.1016/j.rinam.2024.100530","DOIUrl":"10.1016/j.rinam.2024.100530","url":null,"abstract":"<div><div>In this article, a fast two-grid mixed finite element (T-GMFE) algorithm based on a time second-order discrete scheme with parameter <span><math><mi>θ</mi></math></span> is considered to numerically solve a class of two-dimensional nonlinear fractional pseudo-hyperbolic wave models. The weighted and shifted Grünwald difference (WSGD) formula is used to approximate the fractional time derivative at time <span><math><msub><mrow><mi>t</mi></mrow><mrow><mi>n</mi><mo>−</mo><mi>θ</mi></mrow></msub></math></span>, and the spatial direction is approximated by a two-grid <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>1</mn></mrow></msup></math></span>-Galerkin MFE method. The error estimates in both <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>-norm for the fully discrete T-GMFE system are proved. Further, a modified T-GMFE scheme is proposed and the optimal error results are provided. Finally, computing results show the presented T-GMFE method can save computing time and improve the computational efficiency.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100530"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098508","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
A new error analysis for finite element methods for elliptic Neumann boundary control problems with pointwise control constraints
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2025.100544
Susanne C. Brenner, Li-Yeng Sung
{"title":"A new error analysis for finite element methods for elliptic Neumann boundary control problems with pointwise control constraints","authors":"Susanne C. Brenner,&nbsp;Li-Yeng Sung","doi":"10.1016/j.rinam.2025.100544","DOIUrl":"10.1016/j.rinam.2025.100544","url":null,"abstract":"<div><div>We present a new error analysis for finite element methods for a linear-quadratic elliptic optimal control problem with Neumann boundary control and pointwise control constraints. It can be applied to standard finite element methods when the coefficients in the elliptic operator are smooth and also to multiscale finite element methods when the coefficients are rough.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100544"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143098514","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
PINN based on multi-scale strategy for solving Navier–Stokes equation 基于多尺度策略的 PINN，用于求解纳维-斯托克斯方程
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2024.100526
Shirong Li , Shaoyong Lai
{"title":"PINN based on multi-scale strategy for solving Navier–Stokes equation","authors":"Shirong Li ,&nbsp;Shaoyong Lai","doi":"10.1016/j.rinam.2024.100526","DOIUrl":"10.1016/j.rinam.2024.100526","url":null,"abstract":"<div><div>Neural networks combined with automatic differentiation technology provide a fundamental framework for the numerical solution of partial differential equations. This framework constitutes a loss function driven by both data and physical models, significantly enhancing generalization capabilities. Combining the framework and the idea of multi-scale methods in traditional numerical methods, such as domain decomposition and collocation self-adaption, we construct a method of the Physics-Informed Neural Networks (PINNs) based on multi-scale strategy to solve Navier–Stokes equations, and the results are more effective than XPINNs and SAPINNs. The computational efficiency of the proposed method is verified by solving two-dimensional and three-dimensional Navier–Stokes equations.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100526"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143487235","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Structured backward errors for block three-by-three saddle point systems with Hermitian and sparsity block matrices
IF 1.4
Results in Applied Mathematics Pub Date : 2025-02-01 DOI: 10.1016/j.rinam.2025.100546
Bing Tan, Wei Ma
{"title":"Structured backward errors for block three-by-three saddle point systems with Hermitian and sparsity block matrices","authors":"Bing Tan,&nbsp;Wei Ma","doi":"10.1016/j.rinam.2025.100546","DOIUrl":"10.1016/j.rinam.2025.100546","url":null,"abstract":"<div><div>In this paper, we explore the structured backward errors for a class of block three-by-three saddle point systems with Hermitian and sparsity block matrices. We derive an explicit formula for the structured backward errors under the assumption that the inherent matrix structure and sparsity pattern are maintained in the associated perturbation. Moreover, the optimal backward perturbation matrix for achieving structured backward error is constructed. Our analysis further explores the structured backward error when the sparsity structure is not preserved. Numerical experiments show that the computable formulas of structured backward errors are useful for testing the stability of practical algorithms.</div></div>","PeriodicalId":36918,"journal":{"name":"Results in Applied Mathematics","volume":"25 ","pages":"Article 100546"},"PeriodicalIF":1.4,"publicationDate":"2025-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143474560","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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