Finite element discretization of weighted $\Phi$-Laplace problems

TL;DR

This paper investigates finite element methods for weighted $ ext{Phi}$-Laplacian problems, providing error estimates within weighted Orlicz spaces for boundary and obstacle problems.

Contribution

It introduces a finite element discretization framework for weighted $ ext{Phi}$-Laplacian problems using Orlicz space theory, with new error estimates.

Findings

Derived error estimates for boundary value problems

Extended analysis to obstacle problems

Utilized weighted Orlicz and Orlicz--Sobolev spaces

Abstract

We study the finite element approximation of problems involving the weighted $\Phi$-Laplacian, where $\Phi$ is an $N$-function and the weight belongs to the class $A_\Phi$. In particular, we consider a boundary value problem and an obstacle problem and derive error estimates in both cases. The analysis is based on the language of weighted Orlicz and weighted Orlicz--Sobolev spaces.