A Crank–Nicolson ultra-weak discontinuous Galerkin method for solving a unsteady singularly perturbed problem with a shift in space

IF 2.8 2区数学 Q1 MATHEMATICS, APPLIED

Applied Mathematics Letters Pub Date : 2025-09-01 DOI:10.1016/j.aml.2025.109736

Yige Liao , Li-Bin Liu , Xianbing Luo , Guangqing Long

引用次数: 0

Abstract

In this paper, a unsteady singularly perturbed problem (SPP) with a shift in space is studied. The problem is discretized by a ultra-weak discontinuous Galerkin (UWDG) method in space on the Bakhvalov-type (B-type) mesh and by Crank–Nicolson (CN) scheme in time. Through carefully designing numerical fluxes and penalty terms, we rigorously establish the coercivity of the bilinear form associated with the UWDG scheme. Furthermore, based on the

L^{2}

-projection and careful error estimate for Ritz projection, we derive optimal-order convergence estimates. Numerical experiments verify the effectiveness of the method.

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求解空间位移非定常奇摄动问题的Crank-Nicolson超弱不连续Galerkin方法

本文研究了一类具有空间位移的非定常奇摄动问题。在空间上采用bakhvalov型（b型）网格上的超弱不连续Galerkin （UWDG）方法进行离散，在时间上采用Crank-Nicolson （CN）格式进行离散。通过精心设计数值通量和惩罚项，我们严格地建立了与UWDG格式相关的双线性形式的矫顽力。此外，基于l2 -投影和Ritz投影的谨慎误差估计，我们导出了最优阶收敛估计。数值实验验证了该方法的有效性。

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

Applied Mathematics Letters 数学-应用数学

CiteScore

7.70

自引率

5.40%

发文量

347

审稿时长

10 days

期刊介绍： The purpose of Applied Mathematics Letters is to provide a means of rapid publication for important but brief applied mathematical papers. The brief descriptions of any work involving a novel application or utilization of mathematics, or a development in the methodology of applied mathematics is a potential contribution for this journal. This journal''s focus is on applied mathematics topics based on differential equations and linear algebra. Priority will be given to submissions that are likely to appeal to a wide audience.