Weak Galerkin Finite Element Methods for Parabolic Equations

2012/12/14 by Qiaoluan H. Li, Li, Qiaoluan H., Junping Wang +1 · 1 citation
Engineering · #35B45 #35J50 #65N30 #76D07 #Advanced Numerical Methods in Computational Mathematics #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering #Primary 65N15 #Secondary

paper · pdf · doi:10.48550/arxiv.1212.3637

openalex publication_date 2012/12/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 H¹ and L² norms are established. Numerical tests are performed and reported.

Citations

• Weak Galerkin Finite Element Methods on Polytopal Meshes

Cited by

• A C⁰ weak Galerkin method with preconditioning for constrained optimal control problems with general tracking

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