发布求助
文献互助 智能选刊 最新文献

Computational Methods in Applied Mathematics最新文献

筛选
英文 中文
A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control 优化控制下对流偏微分方程的流线型上风 Petrov-Galerkin 降阶方法
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2024-04-23 DOI: 10.1515/cmam-2023-0171
Fabio Zoccolan, Maria Strazzullo, Gianluigi Rozza
{"title":"A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control","authors":"Fabio Zoccolan, Maria Strazzullo, Gianluigi Rozza","doi":"10.1515/cmam-2023-0171","DOIUrl":"https://doi.org/10.1515/cmam-2023-0171","url":null,"abstract":"In this paper we will consider distributed Linear-Quadratic Optimal Control Problems dealing with Advection-Diffusion PDEs for high values of the Péclet number. In this situation, computational instabilities occur, both for steady and unsteady cases. A Streamline Upwind Petrov–Galerkin technique is used in the optimality system to overcome these unpleasant effects. We will apply a finite element method discretization in an <jats:italic>optimize-then-discretize</jats:italic> approach. Concerning the parabolic case, a stabilized space-time framework will be considered and stabilization will also occur in both bilinear forms involving time derivatives. Then we will build Reduced Order Models on this discretization procedure and two possible settings can be analyzed: whether or not stabilization is needed in the online phase, too. In order to build the reduced bases for state, control, and adjoint variables we will consider a Proper Orthogonal Decomposition algorithm in a partitioned approach. It is the first time that Reduced Order Models are applied to stabilized parabolic problems in this setting. The discussion is supported by computational experiments, where relative errors between the FEM and ROM solutions are studied together with the respective computational times.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"54 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140798105","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
HDG Method for Nonlinear Parabolic Integro-Differential Equations 非线性抛物整微分方程的 HDG 方法
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2024-04-12 DOI: 10.1515/cmam-2023-0060
Riya Jain, Sangita Yadav
{"title":"HDG Method for Nonlinear Parabolic Integro-Differential Equations","authors":"Riya Jain, Sangita Yadav","doi":"10.1515/cmam-2023-0060","DOIUrl":"https://doi.org/10.1515/cmam-2023-0060","url":null,"abstract":"The hybridizable discontinuous Galerkin (HDG) method has been applied to a nonlinear parabolic integro-differential equation. The nonlinear functions are considered to be Lipschitz continuous to analyze uniform in time a priori bounds. An extended type Ritz–Volterra projection is introduced and used along with the HDG projection as an intermediate projection to achieve optimal order convergence of <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>O</m:mi> <m:mo>⁢</m:mo> <m:mrow> <m:mo stretchy=\"false\">(</m:mo> <m:msup> <m:mi>h</m:mi> <m:mrow> <m:mi>k</m:mi> <m:mo>+</m:mo> <m:mn>1</m:mn> </m:mrow> </m:msup> <m:mo stretchy=\"false\">)</m:mo> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmam-2023-0060_ineq_0001.png\" /> <jats:tex-math>O(h^{k+1})</jats:tex-math> </jats:alternatives> </jats:inline-formula> when polynomials of degree <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>k</m:mi> <m:mo>≥</m:mo> <m:mn>0</m:mn> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmam-2023-0060_ineq_0002.png\" /> <jats:tex-math>kgeq 0</jats:tex-math> </jats:alternatives> </jats:inline-formula> are used to approximate both the solution and the flux variables. By relaxing the assumptions in the nonlinear variable, super-convergence is achieved by element-by-element post-processing. Using the backward Euler method in temporal direction and quadrature rule to discretize the integral term, a fully discrete scheme is derived along with its error estimates. Finally, with the help of numerical examples in two-dimensional domains, computational results are obtained, which verify our results.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"44 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140593326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 1) 应用数学中的计算方法（CMAM 2022 会议，第 1 部分）
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2024-04-02 DOI: 10.1515/cmam-2024-0030
Michael Feischl, Dirk Praetorius, Michele Ruggeri
{"title":"Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 1)","authors":"Michael Feischl, Dirk Praetorius, Michele Ruggeri","doi":"10.1515/cmam-2024-0030","DOIUrl":"https://doi.org/10.1515/cmam-2024-0030","url":null,"abstract":"This paper introduces the contents of the first of two special issues associated with the 9th International Conference on Computational Methods in Applied Mathematics, which took place from August 29 to September 2, 2022 in Vienna. It comments on the topics and highlights of all twelve papers of the special issue.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"5 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140593320","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Convergence of an Operator Splitting Scheme for Fractional Conservation Laws with Lévy Noise 具有莱维噪声的分数守恒定律的算子分裂方案的收敛性
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2024-04-02 DOI: 10.1515/cmam-2023-0174
Soumya Ranjan Behera, Ananta K. Majee
{"title":"Convergence of an Operator Splitting Scheme for Fractional Conservation Laws with Lévy Noise","authors":"Soumya Ranjan Behera, Ananta K. Majee","doi":"10.1515/cmam-2023-0174","DOIUrl":"https://doi.org/10.1515/cmam-2023-0174","url":null,"abstract":"In this paper, we are concerned with an operator-splitting scheme for linear fractional and fractional degenerate stochastic conservation laws driven by multiplicative Lévy noise. More specifically, using a variant of the classical Kružkov doubling of variables approach, we show that the approximate solutions generated by the splitting scheme converge to the unique stochastic entropy solution of the underlying problems. Finally, the convergence analysis is illustrated by several numerical examples.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"100 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140593366","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Analysis and Numerical Simulation of Time-Fractional Derivative Contact Problem with Friction in Thermo-Viscoelasticity 热-粘弹性中带有摩擦力的时间分数衍生接触问题的分析与数值模拟
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2024-03-25 DOI: 10.1515/cmam-2023-0192
Mustapha Bouallala, EL-Hassan Essoufi, Youssef Ouafik
{"title":"Analysis and Numerical Simulation of Time-Fractional Derivative Contact Problem with Friction in Thermo-Viscoelasticity","authors":"Mustapha Bouallala, EL-Hassan Essoufi, Youssef Ouafik","doi":"10.1515/cmam-2023-0192","DOIUrl":"https://doi.org/10.1515/cmam-2023-0192","url":null,"abstract":"The objective of this study is to analyze a quasistatic frictional contact problem involving the interaction between a thermo-viscoelastic body and a thermally conductive foundation. The constitutive relation in our investigation is constructed using a fractional Kelvin–Voigt model to describe displacement behavior. Additionally, the heat conduction aspect is governed by a time-fractional derivative parameter that is associated with temperature. The contact is modeled using the Signorini condition, which is a version of Coulomb’s law for dry friction. We develop a variational formulation for the problem and establish the existence of its weak solution using a combination of techniques, including the theory of monotone operators, Caputo derivative, Galerkin method, and the Banach fixed point theorem. To demonstrate the effectiveness of our approach, we include several numerical simulations that showcase the performance of the method.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"230 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140300829","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Numerical Study of a Stabilized Hyperbolic Equation Inspired by Models for Bio-Polymerization 受生物聚合模型启发的稳定双曲方程数值研究
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2024-03-25 DOI: 10.1515/cmam-2023-0222
Lisa Davis, Monika Neda, Faranak Pahlevani, Jorge Reyes, Jiajia Waters
{"title":"A Numerical Study of a Stabilized Hyperbolic Equation Inspired by Models for Bio-Polymerization","authors":"Lisa Davis, Monika Neda, Faranak Pahlevani, Jorge Reyes, Jiajia Waters","doi":"10.1515/cmam-2023-0222","DOIUrl":"https://doi.org/10.1515/cmam-2023-0222","url":null,"abstract":"This report investigates a stabilization method for first order hyperbolic differential equations applied to DNA transcription modeling. It is known that the usual unstabilized finite element method contains spurious oscillations for nonsmooth solutions. To stabilize the finite element method the authors consider adding to the first order hyperbolic differential system a stabilization term in space and time filtering. Numerical analysis of the stabilized finite element algorithms and computations describing a few biological settings are studied herein.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"26 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140300953","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Adaptive Multi-level Algorithm for a Class of Nonlinear Problems 一类非线性问题的自适应多级算法
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2024-02-27 DOI: 10.1515/cmam-2023-0088
Dongho Kim, Eun-Jae Park, Boyoon Seo
{"title":"Adaptive Multi-level Algorithm for a Class of Nonlinear Problems","authors":"Dongho Kim, Eun-Jae Park, Boyoon Seo","doi":"10.1515/cmam-2023-0088","DOIUrl":"https://doi.org/10.1515/cmam-2023-0088","url":null,"abstract":"In this article, we propose an adaptive mesh-refining based on the multi-level algorithm and derive a unified a posteriori error estimate for a class of nonlinear problems. We have shown that the multi-level algorithm on adaptive meshes retains quadratic convergence of Newton’s method across different mesh levels, which is numerically validated. Our framework facilitates to use the general theory established for a linear problem associated with given nonlinear equations. In particular, existing a posteriori error estimates for the linear problem can be utilized to find reliable error estimators for the given nonlinear problem. As applications of our theory, we consider the pseudostress-velocity formulation of Navier–Stokes equations and the standard Galerkin formulation of semilinear elliptic equations. Reliable and efficient a posteriori error estimators for both approximations are derived. Finally, several numerical examples are presented to test the performance of the algorithm and validity of the theory developed.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"241 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140009430","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 Phase-Space Discontinuous Galerkin Scheme for the Radiative Transfer Equation in Slab Geometry 板状几何中辐射传输方程的相空间非连续伽勒金方案
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2024-02-20 DOI: 10.1515/cmam-2023-0090
Riccardo Bardin, Fleurianne Bertrand, Olena Palii, Matthias Schlottbom
{"title":"A Phase-Space Discontinuous Galerkin Scheme for the Radiative Transfer Equation in Slab Geometry","authors":"Riccardo Bardin, Fleurianne Bertrand, Olena Palii, Matthias Schlottbom","doi":"10.1515/cmam-2023-0090","DOIUrl":"https://doi.org/10.1515/cmam-2023-0090","url":null,"abstract":"We derive and analyze a symmetric interior penalty discontinuous Galerkin scheme for the approximation of the second-order form of the radiative transfer equation in slab geometry. Using appropriate trace lemmas, the analysis can be carried out as for more standard elliptic problems. Supporting examples show the accuracy and stability of the method also numerically, for different polynomial degrees. For discretization, we employ quad-tree grids, which allow for local refinement in phase-space, and we show exemplary that adaptive methods can efficiently approximate discontinuous solutions. We investigate the behavior of hierarchical error estimators and error estimators based on local averaging.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"73 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-02-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139922783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Convergence of Adaptive Crouzeix–Raviart and Morley FEM for Distributed Optimal Control Problems 分布式优化控制问题的自适应 Crouzeix-Raviart 和 Morley 有限元收敛性
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2024-02-09 DOI: 10.1515/cmam-2023-0083
Asha K. Dond, Neela Nataraj, Subham Nayak
{"title":"Convergence of Adaptive Crouzeix–Raviart and Morley FEM for Distributed Optimal Control Problems","authors":"Asha K. Dond, Neela Nataraj, Subham Nayak","doi":"10.1515/cmam-2023-0083","DOIUrl":"https://doi.org/10.1515/cmam-2023-0083","url":null,"abstract":"This article discusses the quasi-optimality of adaptive nonconforming finite element methods for distributed optimal control problems governed by 𝑚-harmonic operators for <jats:inline-formula> <jats:alternatives> <m:math xmlns:m=\"http://www.w3.org/1998/Math/MathML\"> <m:mrow> <m:mi>m</m:mi> <m:mo>=</m:mo> <m:mrow> <m:mn>1</m:mn> <m:mo>,</m:mo> <m:mn>2</m:mn> </m:mrow> </m:mrow> </m:math> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" xlink:href=\"graphic/j_cmam-2023-0083_ineq_0001.png\" /> <jats:tex-math>m=1,2</jats:tex-math> </jats:alternatives> </jats:inline-formula>. A variational discretization approach is employed and the state and adjoint variables are discretized using nonconforming finite elements. Error equivalence results at the continuous and discrete levels lead to a priori and a posteriori error estimates for the optimal control problem. The general axiomatic framework that includes stability, reduction, discrete reliability, and quasi-orthogonality establishes the quasi-optimality. Numerical results demonstrate the theoretically predicted orders of convergence and the efficiency of the adaptive estimator.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"45 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139769478","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
Weak Convergence of the Rosenbrock Semi-implicit Method for Semilinear Parabolic SPDEs Driven by Additive Noise 加性噪声驱动的半线性抛物 SPDE 的罗森布洛克半隐式方法的弱收敛性
IF 1.3 4区 数学
Computational Methods in Applied Mathematics Pub Date : 2024-01-30 DOI: 10.1515/cmam-2023-0055
Jean Daniel Mukam, Antoine Tambue
{"title":"Weak Convergence of the Rosenbrock Semi-implicit Method for Semilinear Parabolic SPDEs Driven by Additive Noise","authors":"Jean Daniel Mukam, Antoine Tambue","doi":"10.1515/cmam-2023-0055","DOIUrl":"https://doi.org/10.1515/cmam-2023-0055","url":null,"abstract":"This paper aims to investigate the weak convergence of the Rosenbrock semi-implicit method for semilinear parabolic stochastic partial differential equations (SPDEs) driven by additive noise. We are interested in SPDEs where the nonlinear part is stronger than the linear part, also called stochastic reaction dominated transport equations. For such SPDEs, many standard numerical schemes lose their stability properties. Exponential Rosenbrock and Rosenbrock-type methods were proved to be efficient for such SPDEs, but only their strong convergence were recently analyzed. Here, we investigate the weak convergence of the Rosenbrock semi-implicit method. We obtain a weak convergence rate which is twice the rate of the strong convergence. Our error analysis does not rely on Malliavin calculus, but rather only uses the Kolmogorov equation and the smoothing properties of the resolvent operator resulting from the Rosenbrock semi-implicit approximation.","PeriodicalId":48751,"journal":{"name":"Computational Methods in Applied Mathematics","volume":"6 1","pages":""},"PeriodicalIF":1.3,"publicationDate":"2024-01-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139646763","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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
首页 上一页 下一页 尾页
0
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整，为了账户安全，请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
请完成安全验证×
相关产品
×
本文献相关产品
联系我们：info@booksci.cn Book学术提供免费学术资源搜索服务，方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信