Applied Numerical Mathematics最新文献

Numerical approximations for a hyperbolic integrodifferential equation with a non-positive variable-sign kernel and nonlinear-nonlocal damping

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-26 DOI: 10.1016/j.apnum.2025.02.018

Wenlin Qiu , Xiangcheng Zheng , Kassem Mustapha

引用次数: 0

Well-balanced and positivity-preserving wet-dry front reconstruction scheme for Ripa models

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-25 DOI: 10.1016/j.apnum.2025.02.014

Xue Wang , Guoxian Chen

{"title":"Well-balanced and positivity-preserving wet-dry front reconstruction scheme for Ripa models","authors":"Xue Wang , Guoxian Chen","doi":"10.1016/j.apnum.2025.02.014","DOIUrl":"10.1016/j.apnum.2025.02.014","url":null,"abstract":"<div><div>This paper explores the reconstruction of wet-dry fronts (WDF) for solving both one-dimensional (1D) and two-dimensional (2D) Ripa systems, with a particular emphasis on the influence of temperature. Our aim is to develop a well-balanced numerical scheme that not only preserves the steady state but also ensures the positivity of both water height and temperature. By employing conservative variables for reconstruction instead of equilibrium variables, we have achieved a significant doubling of the CFL number for fully flooded cells. We have refined the original 1D WDF reconstruction method and further enhanced the corresponding 2D scheme. The conservation principle and linearity observed in the wet region of partially flooded cells indicate a constant cell-wise velocity and temperature. Additionally, we introduce a novel draining time approach to adjust the numerical flux in an upwind manner, ensuring both stability and efficiency, even for partially flooded cells. Numerical examples are presented to demonstrate the well-balanced property, high-order accuracy, and positivity-preserving characteristics of our proposed method. These examples also showcase the method's ability to capture small perturbations in the lake-at-rest steady state, highlighting its potential for practical applications.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"213 ","pages":"Pages 38-60"},"PeriodicalIF":2.2,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143507961","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}

引用次数: 0

Drug release from polymeric platforms for non smooth solutions

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-25 DOI: 10.1016/j.apnum.2025.02.016

J.S. Borges , G.C.M. Campos , J.A. Ferreira , G. Romanazzi

{"title":"Drug release from polymeric platforms for non smooth solutions","authors":"J.S. Borges , G.C.M. Campos , J.A. Ferreira , G. Romanazzi","doi":"10.1016/j.apnum.2025.02.016","DOIUrl":"10.1016/j.apnum.2025.02.016","url":null,"abstract":"<div><div>This paper aims to conclude a sequence of works focused in the numerical study of a system of partial differential equations in a nonuniform grid that can be used to describe the drug release from polymeric platforms. The drug release is a consequence of the non-Fickian fluid uptake, the dissolution process and the Fickian drug transport. The development of a computational tool and its theoretical convergence support was the common driven force. In a previous work from the authors, second order error estimates were established for the numerical approximations for the solvent, solid drug and dissolved drug considering severe smoothness assumption on the solutions: the solvent and the dissolve drug were <span><math><msup><mrow><mi>C</mi></mrow><mrow><mn>4</mn></mrow></msup></math></span>- functions. In the present work, our aim is to establish second order estimates for the same variables reducing the smoothness assumption, namely, we assume that the solvent and the dissolved drug are <span><math><msup><mrow><mi>H</mi></mrow><mrow><mn>3</mn></mrow></msup></math></span>- functions. Numerical experiments illustrating the obtained theoretical results are also included.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"213 ","pages":"Pages 12-37"},"PeriodicalIF":2.2,"publicationDate":"2025-02-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143508679","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}

引用次数: 0

A novel projection-based method for monotone equations with Aitken Δ2 acceleration and its application to sparse signal restoration

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-21 DOI: 10.1016/j.apnum.2025.02.013

Ahmad Kamandi

引用次数: 0

Convergence analysis of weak Galerkin finite element variable-time-step BDF2 implicit scheme for parabolic equations

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-21 DOI: 10.1016/j.apnum.2025.02.015

Chenxing Li , Fuzheng Gao , Jintao Cui

引用次数: 0

A decoupled nonconforming finite element method for biharmonic equation in three dimensions

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-19 DOI: 10.1016/j.apnum.2025.02.012

Xuewei Cui, Xuehai Huang

引用次数: 0

A mixed discontinuous Galerkin method for the Biot equations

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-19 DOI: 10.1016/j.apnum.2025.02.011

Jing Wen

{"title":"A mixed discontinuous Galerkin method for the Biot equations","authors":"Jing Wen","doi":"10.1016/j.apnum.2025.02.011","DOIUrl":"10.1016/j.apnum.2025.02.011","url":null,"abstract":"<div><div>The Biot model is a coupling problem between the elastic media material with small deformation and porous media fluid flow, its mixed formulation uses the pore pressure, fluid flux, displacement as well as total stress tensor as the primary unknown variables. In this article, combining the discontinuous Galerkin method and the backward Euler method, we propose a mixed discontinuous Galerkin (MDG) method for the mixed Biot equations, it is based on coupling two MDG methods for each subproblem: the MDG method for the porous media fluid flow subproblem and the Hellinger-Reissner formulation of linear elastic subproblem. Then, we prove the well-posedness and the optimal priori error estimates for the MDG method under suitable norms. In particular, the optimal convergence rate of the pressure, displacement and stress tensor in discrete <span><math><msup><mrow><mi>L</mi></mrow><mrow><mo>∞</mo></mrow></msup><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> norm and the fluid flux in discrete <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> norm are proved when the storage coefficient <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is strictly positive. Similarly, we deduce the optimal convergence rate of all variables in discrete <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>(</mo><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup><mo>)</mo></math></span> norm when <span><math><msub><mrow><mi>c</mi></mrow><mrow><mn>0</mn></mrow></msub></math></span> is nonnegative. Finally, some numerical experiments are given to examine the convergence analysis.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 283-299"},"PeriodicalIF":2.2,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143454013","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}

引用次数: 0

An efficient two-grid algorithm based on Newton iteration for the stationary inductionless magnetohydrodynamic system

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-19 DOI: 10.1016/j.apnum.2025.02.009

Yande Xia , Yun-Bo Yang

{"title":"An efficient two-grid algorithm based on Newton iteration for the stationary inductionless magnetohydrodynamic system","authors":"Yande Xia , Yun-Bo Yang","doi":"10.1016/j.apnum.2025.02.009","DOIUrl":"10.1016/j.apnum.2025.02.009","url":null,"abstract":"<div><div>In this paper, we propose and analyze a two-grid algorithm based on Newton iteration for solving the stationary inductionless magnetohydrodynamic system. The method involves first solving a small nonlinear system on a coarse grid with grid size <em>H</em>, followed by solving two linear problems on a fine grid with grid size <em>h</em>. These linear problems share the same stiffness matrix but differ only in their right-hand sides. The scaling between the coarse and fine grids is improved by our new method, while the approximate solution retains the same order of convergence as that observed in conventional methods. Furthermore, <span><math><msub><mrow><mi>H</mi></mrow><mrow><mn>0</mn></mrow></msub><mo>(</mo><mrow><mi>div</mi></mrow><mo>,</mo><mi>Ω</mi><mo>)</mo><mo>×</mo><msubsup><mrow><mi>L</mi></mrow><mrow><mn>0</mn></mrow><mrow><mn>2</mn></mrow></msubsup><mo>(</mo><mi>Ω</mi><mo>)</mo></math></span>-conforming finite element pairs are utilized to discretize the current density and electric potential, ensuring that the discrete current density is exactly divergence-free. Stability and convergence analyses are rigorously derived, and <span><math><msup><mrow><mi>L</mi></mrow><mrow><mn>2</mn></mrow></msup></math></span>-error estimates for the velocity are provided. Numerical experiments are presented to verify the theoretical predictions and demonstrate the efficiency of the proposed method.</div></div>","PeriodicalId":8199,"journal":{"name":"Applied Numerical Mathematics","volume":"212 ","pages":"Pages 312-332"},"PeriodicalIF":2.2,"publicationDate":"2025-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"143480232","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}

引用次数: 0

Functional equation arising in behavioral sciences: solvability and collocation scheme in Hölder spaces

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-18 DOI: 10.1016/j.apnum.2025.02.010

Josefa Caballero , Hanna Okrasińska-Płociniczak , Łukasz Płociniczak , Kishin Sadarangani

引用次数: 0

Estimating the growth of solutions of linear delayed difference and differential equations by alternating maximization

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-17 DOI: 10.1016/j.apnum.2025.02.008

Miloud Sadkane , Roger B. Sidje

引用次数: 0