Work

A posteriori error bounds for finite element approximations of steady-state mean field games

Year: 2025

Type: article

Abstract: We analyse a posteriori error bounds for stabilised finite element discretisations of second-order steady-state mean field games. We prove the local equivalence between the $H^{1}$-norm of the error and the dual norm of the residual. We then derive reliable and efficient estimators for a broad class of stabilised first-order finite element methods. We also show that in the case of affine-preserving stabilisations, the estimator can be further simplified to the standard residual estimator. Numerical experiments illustrate the computational gains in efficiency and accuracy from the estimators in the context of adaptive methods.

Source: IMA Journal of Numerical Analysis

DOI: 10.1093/imanum/draf107

Authors: Yohance A P Osborne, Iain Smears, Harry Wells

Institutions: Durham University, University College London

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,718

Funder: Engineering and Physical Sciences Research Council