The two-grid hybrid high-order method for the nonlinear strongly damped wave equation on polygonal mesh and its reduced-order model

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

Applied Numerical Mathematics Pub Date : 2024-12-16 DOI:10.1016/j.apnum.2024.12.006

Lu Wang, Youjun Tan, Minfu Feng

引用次数: 0

Abstract

This paper introduces the hybrid high-order (HHO) method for solving the nonlinear strongly damped wave equation. We comprehensively analyze the semi-discrete and fully-discrete implicit schemes, including energy and

L^{2}

norm, with convergence rates of

m + 1

and

m + 2

in space (

m \geq 0

), respectively. In addition, we combine the two-grid algorithm (TGA) with the HHO method (TGA-HHO) to improve computational efficiency and analyze the TGA-HHO method. To improve the computational efficiency further, we combine the proper orthogonal decomposition (POD) technique with the TGA-HHO method (POD-TGA-HHO). Finally, we provide numerical examples to validate the effectiveness of the HHO, TGA-HHO, and POD-TGA-HHO algorithms.

查看原文本刊更多论文

求助全文

约1分钟内获得全文求助全文

来源期刊

Applied Numerical Mathematics 数学-应用数学

CiteScore

5.60

自引率

7.10%

发文量

225

审稿时长

7.2 months

期刊介绍： The purpose of the journal is to provide a forum for the publication of high quality research and tutorial papers in computational mathematics. In addition to the traditional issues and problems in numerical analysis, the journal also publishes papers describing relevant applications in such fields as physics, fluid dynamics, engineering and other branches of applied science with a computational mathematics component. The journal strives to be flexible in the type of papers it publishes and their format. Equally desirable are: (i) Full papers, which should be complete and relatively self-contained original contributions with an introduction that can be understood by the broad computational mathematics community. Both rigorous and heuristic styles are acceptable. Of particular interest are papers about new areas of research, in which other than strictly mathematical arguments may be important in establishing a basis for further developments. (ii) Tutorial review papers, covering some of the important issues in Numerical Mathematics, Scientific Computing and their Applications. The journal will occasionally publish contributions which are larger than the usual format for regular papers. (iii) Short notes, which present specific new results and techniques in a brief communication.