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arXiv · 2507.12742

Quasi-optimality of the Crouzeix-Raviart FEM for p-Laplace-type problems

Johannes Storn
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Abstract

We verify quasi-optimality of the Crouzeix-Raviart FEM for nonlinear problems of $p$-Laplace type. More precisely, we show that the error of the Crouzeix-Raviart FEM with respect to a quasi-norm is bounded from above by a uniformly bounded constant times the best-approximation error plus a data oscillation term. As a byproduct, we verify a novel more localized a priori error estimate for the conforming lowest-order Lagrange FEM.

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Johannes Storn. 2026-04-02. Quasi-optimality of the Crouzeix-Raviart FEM for p-Laplace-type problems. https://arxiv.org/abs/2507.12742

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