Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients

TL;DR

This paper introduces a multigrid preconditioner tailored for nonconforming discretizations of elliptic problems with jump coefficients, demonstrating robustness and near-optimal performance through numerical tests.

Contribution

It proposes a novel multigrid preconditioner using conforming subspaces for nonconforming discretizations with jump coefficients, enhancing solver efficiency.

Findings

Robustness against coefficient jumps

Near-optimal convergence with respect to degrees of freedom

Effective preconditioning for nonconforming discretizations

Abstract

In this paper, we present a multigrid preconditioner for solving the linear system arising from the piecewise linear nonconforming Crouzeix-Raviart discretization of second order elliptic problems with jump coefficients. The preconditioner uses the standard conforming subspaces as coarse spaces. Numerical tests show both robustness with respect to the jump in the coefficient and near-optimality with respect to the number of degrees of freedom.