Variational Approximation in Modular Spaces by Using Finite Element Method Approach

Abstract

In this paper, we shall study the polynomial approximation in a more general setting namely to consider the Orlicz-Sobolev spaces $W^k{L}_M(\Omega ).$ We study the local and global interpolation estimate and we will show the finite element error estimate for a nonlinear elliptic problem where we establish a generalization of Cea’s Theorem and we prove the modular convergence of the gradient, then we present the existence result and its proof.

Keywords:

• Finite element method
• interpolation operators
• nonlinear elliptic problem
• Orlicz spaces