Weak Galerkin Finite Element Methods for Parabolic Equations

TL;DR

This paper introduces a weak Galerkin finite element method for parabolic equations that uses discontinuous functions, preserves energy, and achieves optimal error estimates, supported by numerical validation.

Contribution

It develops a novel weak Galerkin approach for parabolic equations, enabling discontinuous approximations and energy conservation, with rigorous error analysis.

Findings

Optimal error estimates in H^1 and L^2 norms

Method preserves energy conservation law

Numerical tests confirm theoretical results

Abstract

A newly developed weak Galerkin method is proposed to solve parabolic equations. This method allows the usage of totally discontinuous functions in approximation space and preserves the energy conservation law. Both continuous and discontinuous time weak Galerkin finite element schemes are developed and analyzed. Optimal order error estimates in both H^1 and L^2 norms are established. Numerical tests are performed and reported.