Error Analysis of the Second-Order Serendipity Virtual Element Method for Semilinear Pseudo-Parabolic Equations on Curved Domains
Year: 2024
Author: Yang Xu, Zhenguo Zhou, Jingjun Zhao
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 6 : pp. 1743–1776
Abstract
The second-order serendipity virtual element method is studied for the semilinear pseudo-parabolic equations on curved domains in this paper. Nonhomogeneous Dirichlet boundary conditions are taken into account, the existence and uniqueness are investigated for the weak solution of the nonhomogeneous initial-boundary value problem. The Nitsche-based projection method is adopted to impose the boundary conditions in a weak way. The interpolation operator is used to deal with the nonlinear term. The Crank-Nicolson scheme is employed to discretize the temporal variable. There are two main features of the proposed scheme: (i) the internal degrees of freedom are avoided no matter what type of mesh is utilized, and (ii) the Jacobian is simple to calculate when Newton’s iteration method is applied to solve the fully discrete scheme. The error estimates are established for the discrete schemes and the theoretical results are illustrated through some numerical examples.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jcm.2307-m2023-0012
Journal of Computational Mathematics, Vol. 42 (2024), Iss. 6 : pp. 1743–1776
Published online: 2024-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 34
Keywords: Semilinear pseudo-parabolic equation Serendipity virtual element method Projection method Curved domain.
Author Details
Yang Xu Email
Zhenguo Zhou Email
Jingjun Zhao Email