Conforming Virtual Element Methods for Sobolev Equations

Xu, Yang; Zhou, Zhenguo; Zhao, Jingjun

doi:10.1007/s10915-022-01997-3

Cited by 9 publications

(1 citation statement)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A more comprehensive survey of numerical methods for various types of pseudo-parabolic equations can be found in [1]. In recent years, numerical methods that can deal with polygonal or polyhedral meshes have become important issues in the field of scientific computing, and such methods have been used to numerically solve pseudo-parabolic equations, including weak Galerkin methods [17], hybrid high-order methods [34] and virtual element methods [35].…”

Section: Introductionmentioning

confidence: 99%

Error Analysis of the Second-Order Serendipity Virtual Element Method for Semilinear Pseudo-Parabolic Equations on Curved Domains

Xu,

null,

Zhao

2024

JCM

View full text Add to dashboard Cite

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 Nitschebased 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.

show abstract