Error Analysis of the Second-Order Serendipity Virtual Element Method for Semilinear Pseudo-Parabolic Equations on Curved Domains (Journal of Computational Mathematics, 2024)
The second-order serendipity virtual element method is studied for the semilinearpseudo-parabolic equations on curved domains in this paper. Nonhomogeneous Dirichletboundary conditions are taken into account, the existence and uniqueness are investigatedfor 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-Nicolsonscheme is employed to discretize the temporal variable. There are two main features ofthe proposed scheme: (i) the internal degrees of freedom are avoided no matter what typeof mesh is utilized, and (ii) the Jacobian is simple to calculate when Newton’s iterationmethod is applied to solve the fully discrete scheme. The error estimates are establishedfor the discrete schemes and the theoretical results are illustrated through some numericalexamples.
Keywords: Semilinear pseudo-parabolic equation; Serendipity virtual element method; Projection method; Curved domain.