Work

Minimal residual discretization of a class of fully nonlinear elliptic PDE

Year: 2025

Type: article

Abstract: This work introduces finite-element methods for a class of elliptic fully nonlinear partial differential equations. They are based on a minimal residual principle that builds upon the Alexandrov–Bakelman–Pucci estimate. Under rather general structural assumptions on the operator, convergence of $C^{1}$ conforming and discontinuous Galerkin methods is proven in the $L^{^\infty} $ norm. Numerical experiments on the performance of adaptive mesh refinement driven by local information of the residual in two and three space dimensions are provided.

Source: IMA Journal of Numerical Analysis

DOI: 10.1093/imanum/draf075

Authors: Dietmar Gallistl, Ngoc Tien Tran

Institutions: Friedrich Schiller University Jena, University of Augsburg

Language: English

Topic: Advanced Numerical Methods in Computational Mathematics

Subfield: Computational Mechanics

Field: Engineering

Domain: Physical Sciences

Open Access status: green

Funders: European Commission, Horizon 2020 Framework Programme

Awards: G434337789, G5396124100