Work

A priori and a posteriori error estimates for discontinuous Galerkin time-discrete methods via maximal regularity

Year: 2025

Type: article

Abstract: The maximal regularity property of discontinuous Galerkin methods for linear parabolic equations is used together with variational techniques to establish a priori and a posteriori error estimates of optimal order under optimal regularity assumptions. The analysis is set in the maximal regularity framework of UMD Banach spaces. Similar results were proved in an earlier work, based on the consistency analysis of Radau IIA methods. The present error analysis, which is based on variational techniques, is of independent interest, but the main motivation is that it extends to nonlinear parabolic equations; in contrast to the earlier work. Both autonomous and nonautonomous linear equations are considered.

Source: BIT Numerical Mathematics

DOI: 10.1007/s10543-025-01094-5

Authors: Georgios Akrivis, Stig Larsson

Institutions: University of Ioannina, FORTH Institute of Applied and Computational Mathematics, Chalmers University of Technology, University of Gothenburg

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,190

Funders: Chalmers Tekniska Högskola, Vetenskapsrådet