A Posteriori Error Estimates for Parabolic Partial Differential Equations on Stationary Surfaces

IF 3.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Numerical Analysis Pub Date : 2026-08-17 DOI:10.1137/25m1784466

Balázs Kovács, Michael Lantelme

引用次数: 0

Abstract

SIAM Journal on Numerical Analysis, Volume 64, Issue 4, Page 1705-1732, August 2026.
Abstract. This paper develops and discusses a residual-based a posteriori error estimator for parabolic surface partial differential equations on closed stationary surfaces. The full discretization uses the surface finite element method in space and the backward Euler method in time. The proposed error indicator bounds the error quantities globally in space from above and below, and globally in time from above and locally from below. Based on the derived error indicator, a space-time adaptive algorithm is proposed. Numerical experiments illustrate and complement the theory.

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平稳曲面上抛物型偏微分方程的后验误差估计

SIAM数值分析杂志，64卷，第4期，第1705-1732页，2026年8月。摘要。本文发展并讨论了一个基于残差的后验误差估计方法。完全离散化在空间上采用曲面有限元法，在时间上采用倒推欧拉法。所提出的误差指标从上到下在空间上限定全局误差量，从上到下在时间上限定全局误差量，从下到局部误差量。在导出误差指标的基础上，提出了一种时空自适应算法。数值实验对理论进行了验证和补充。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

SIAM Journal on Numerical Analysis 数学-应用数学

CiteScore

4.80

自引率

6.90%

发文量

110

审稿时长

4-8 weeks

期刊介绍： SIAM Journal on Numerical Analysis (SINUM) contains research articles on the development and analysis of numerical methods. Topics include the rigorous study of convergence of algorithms, their accuracy, their stability, and their computational complexity. Also included are results in mathematical analysis that contribute to algorithm analysis, and computational results that demonstrate algorithm behavior and applicability.