Journals
Resources
About Us
Open Access

An Explicit Superconvergent Weak Galerkin Finite Element Method for the Heat Equation

An Explicit Superconvergent Weak Galerkin Finite Element Method for the Heat Equation

Year:    2025

Author:    Fuzheng Gao, Shangyou Zhang

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 2 : pp. 538–553

Abstract

An explicit two-order superconvergent weak Galerkin finite element method is designed and analyzed for the heat equation on triangular and tetrahedral grids. For two-order superconvergent $P_k$ weak Galerkin finite elements, the auxiliary inter-element functions must be $P_{k+1}$ polynomials. In order to achieve the superconvergence, the usual $H^1$-stabilizer must be also eliminated. For time-explicit weak Galerkin method, a time-stabilizer is added, on which the time-derivative of the auxiliary variables can be defined. But for the two-order superconvergent weak Galerkin finite elements, the time-stabilizer must be very weak, an $H^{−2}$-like inner-product instead of an $L^2$-like inner-product. We show the two-order superconvergence for both semi-discrete and fully-discrete schemes. Numerical examples are provided.

You do not have full access to this article.

Already a Subscriber? Sign in as an individual or via your institution

Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2023-0290

Advances in Applied Mathematics and Mechanics, Vol. 17 (2025), Iss. 2 : pp. 538–553

Published online:    2025-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    16

Keywords:    Parabolic equations finite element weak Galerkin method polytopal mesh.

Author Details

Fuzheng Gao

Shangyou Zhang