Emergent Mind
Error analysis for a Crouzeix-Raviart approximation of the $p$-Dirichlet problem
(2210.12116)
Published Oct 21, 2022
in
math.NA
and
cs.NA
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.
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