Work

A Posteriori Error Analysis of the Virtual Element Method for Second-Order Quasilinear Elliptic PDEs

Year: 2025

Type: article

Abstract: In this paper we develop a C 0 {C^{0}} -conforming virtual element method (VEM) for a class of second-order quasilinear elliptic PDEs in two dimensions. We present a posteriori error analysis for this problem and derive a residual based error estimator. The estimator is fully computable and we prove upper and lower bounds of the error which are explicit in the local mesh size. We use the estimator to drive an adaptive mesh refinement algorithm. A handful of numerical test problems are carried out to study the performance of the proposed error indicator.

Source: Computational Methods in Applied Mathematics

DOI: 10.1515/cmam-2024-0153

Authors: Scott Congreve, Alice Hodson

Institution: Charles University

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: Univerzita Karlova v Praze, Grantová Agentura, Univerzita Karlova

Award: G8919054045