TY - JOUR
T1 - Error Analysis of the Second-Order Serendipity Virtual Element Method for Semilinear Pseudo-Parabolic Equations on Curved Domains
AU - Xu , Yang
AU - Zhou , Zhenguo
AU - Zhao , Jingjun
JO - Journal of Computational Mathematics
VL - 6
SP - 1743
EP - 1776
PY - 2024
DA - 2024/11
SN - 42
DO - http://doi.org/10.4208/jcm.2307-m2023-0012
UR - https://global-sci.org/intro/article_detail/jcm/23514.html
KW - Semilinear pseudo-parabolic equation, Serendipity virtual element method,
Projection method, Curved domain.
AB - <p style="text-align: justify;">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.</p>