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

2025/07/17 by Johannes Storn, Storn, Johannes
Engineering · #Numerical methods in engineering #Advanced Numerical Methods in Computational Mathematics #Soil, Finite Element Methods

paper · pdf · doi:10.48550/arxiv.2507.12742

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.

Citations

• Guaranteed upper bounds for iteration errors and modified Kacanov schemes via discrete duality
• Global regularity for nonlinear systems with symmetric gradients
• Crouzeix-Raviart finite element method for non-autonomous variational problems with Lavrentiev gap
• How to prove the discrete reliability for nonconforming finite element\n methods
• Adaptive nonconforming Crouzeix-Raviart FEM for eigenvalue problems
• Two-level additive Schwarz preconditioners for nonconforming finite element methods

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