Error analysis for a Crouzeix-Raviart approximation of the $p$-Dirichlet problem

Abstract

In the present paper, we examine a Crouzeix-Raviart approximation for non-linear partial differential equations having a $(p,\delta )$-structure for some $p\in (1,\infty )$ and $\delta \ge 0$. We establish a priori error estimates, which are optimal for all $p\in (1,\infty )$ and $\delta \ge 0$, medius error estimates, i.e., best-approximation results, and a primal-dual a posteriori error estimate, which is both reliable and efficient. The theoretical findings are supported by numerical experiments.

27 pages, 2 tables, 1 figure, published in Journal of Numerical Mathematics

References in corpus (1)

• Error analysis for a Crouzeix-Raviart approximation of the $p$-Dirichlet problem

Cited by in corpus (2)

• Error analysis for a Crouzeix-Raviart approximation of the $p$-Dirichlet problem
• Discrete weak duality of hybrid high-order methods for convex minimization problems