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A Weak Galerkin Method with $C^0$ Element for Fourth Order Linear Parabolic Equation

A Weak Galerkin Method with $C^0$ Element for Fourth Order Linear Parabolic Equation
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Year:    2019

Author:    Shimin Chai, Yongkui Zou, Wenju Zhao

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 467–485

Abstract

This paper is concerned with the $C^0$ weak Galerkin finite element method for a fourth order linear parabolic equation. The method is based on the construction of a discrete weak Laplacian operator. The error estimates are obtained for semi-discrete weak Galerkin finite element method. Numerical results are presented to confirm the theory.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2018-0028

Advances in Applied Mathematics and Mechanics, Vol. 11 (2019), Iss. 2 : pp. 467–485

Published online:    2019-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Fourth order parabolic equation weak Galerkin error estimate.

Author Details

Shimin Chai

Yongkui Zou

Wenju Zhao

  1. A C0 weak Galerkin method for linear Cahn–Hilliard–Cook equation with random initial condition

    Chai, Shimin | Wang, Yu | Zhao, Wenju | Zou, Yongkui

    Applied Mathematics and Computation, Vol. 414 (2022), Iss. P.126659

    https://doi.org/10.1016/j.amc.2021.126659 [Citations: 1]

  2. Optimal convergence analysis of weak Galerkin finite element methods for parabolic equations with lower regularity

    Liu, Xuan | Zou, Yongkui | Chai, Shimin | Wang, Huimin

    Numerical Algorithms, Vol. 97 (2024), Iss. 3 P.1323

    https://doi.org/10.1007/s11075-024-01751-w [Citations: 0]

  3. A hybridized weak Galerkin finite element scheme for linear elasticity problem

    Zhao, Lidan | Wang, Ruishu | Zou, Yongkui

    Journal of Computational and Applied Mathematics, Vol. 425 (2023), Iss. P.115024

    https://doi.org/10.1016/j.cam.2022.115024 [Citations: 2]

  4. A family of interior-penalized weak Galerkin methods for second-order elliptic equations

    Liu, Kaifang | Song, Lunji

    AIMS Mathematics, Vol. 6 (2021), Iss. 1 P.500

    https://doi.org/10.3934/math.2021030 [Citations: 2]