Diagonally implicit Runge-Kutta schemes: Discrete energy-balance laws and compactness properties-Reference-Cited by-同舟云学术

Diagonally implicit Runge-Kutta schemes: Discrete energy-balance laws and compactness properties

Published:2022-12-25 Issue:0 Volume:0 Page:
ISSN:1570-2820
Container-title:Journal of Numerical Mathematics
language:en
Short-container-title:

Author:

Salgado Abner J.¹,Tomas Ignacio²

Affiliation:

1. Department of Mathematics, University of Tennessee , Knoxville TN 37996 , USA

2. Department of Mathematics and Statistics, Texas Tech University Lubbock , TX 79409 , United States

Abstract

Abstract We study diagonally implicit Runge-Kutta (DIRK) schemes when applied to abstract evolution problems that fit into the Gelfand-triple framework. We introduce novel stability notions that are well-suited to this setting and provide simple, necessary and sufficient, conditions to verify that a DIRK scheme is stable in our sense and in Bochner-type norms. We use several popular DIRK schemes in order to illustrate cases that satisfy the required structural stability properties and cases that do not. In addition, under some mild structural conditions on the problem we can guarantee compactness of families of discrete solutions with respect to time discretization.

Publisher

Walter de Gruyter GmbH

Subject

Computational Mathematics,Numerical Analysis

Link

https://www.degruyter.com/document/doi/10.1515/jnma-2022-0069/pdf

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