Applied Numerical Mathematics最新文献_第3页

Drug release from polymeric platforms for non smooth solutions 非光滑溶液的聚合物平台药物释放

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 一种新的具有Aitken Δ2加速度的单调方程投影方法及其在稀疏信号恢复中的应用

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 抛物型方程弱Galerkin有限元变时步BDF2隐式格式的收敛性分析

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 三维双调和方程的解耦非协调有限元法

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 Biot方程的混合不连续Galerkin方法

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 静止无感应磁流体动力系统基于牛顿迭代的高效两网格算法

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 行为科学中出现的泛函方程：Hölder空间的可解性和搭配方案

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 用交替最大化法估计线性时滞差分和微分方程解的增长

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

An inverse problem of Robin coefficient identification in parabolic equations with interior degeneracy from terminal observation data 基于终端观测资料的内简并抛物方程Robin系数辨识反问题

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-13 DOI: 10.1016/j.apnum.2025.02.007

H. Ould Sidi , A.S. Hendy , M.M. Babatin , L. Qiao , M.A. Zaky

引用次数: 0

Two fourth-order conservative compact difference schemes for the generalized Korteweg–de Vries–Benjamin Bona Mahony equation 广义Korteweg-de Vries-Benjamin Bona Mahony方程的两个四阶保守紧致差分格式

IF 2.2 2区数学

Applied Numerical Mathematics Pub Date : 2025-02-12 DOI: 10.1016/j.apnum.2025.02.005

Xin Zhang , Yuanfeng Jin

引用次数: 0