A primal discontinuous Galerkin method with static condensation on very general meshes

TL;DR

This paper introduces an efficient primal discontinuous Galerkin method with static condensation for second order elliptic equations on complex meshes, maintaining optimal accuracy while reducing computational costs.

Contribution

The paper presents a novel static condensation technique for a primal DG method that preserves optimal error estimates on very general meshes.

Findings

Numerical experiments confirm the accuracy of the new method.

The method reduces computational complexity compared to classical approaches.

Optimal error estimates are maintained despite modifications.

Abstract

We propose an efficient variant of a primal Discontinuous Galerkin method with interior penalty for the second order elliptic equations on very general meshes (polytopes with eventually curved boundaries). Efficiency, especially when higher order polynomials are used, is achieved by static condensation, i.e. a local elimination of certain degrees of freedom element by element. This alters the original method in a way that preserves the optimal error estimates. Numerical experiments confirm that the solutions produced by the new method are indeed very close to that produced by the classical one.