Virtual element method for the Sobolev equations
Copyright policy )Virtual element method for the Sobolev equations
The virtual element method for the Sobolev equations is proposed in this paper, where the semi‐discrete scheme and the fully discrete scheme are both discussed. With the help of the energy projection operator defined by the discrete bilinear form, the corresponding optimal error estimates in the norm and semi‐norm for both the semi‐discrete solution and the fully discrete solution are deduced. Finally, three numerical examples are carried out to verify the theoretical results.
- Zhengzhou University China (People's Republic of)
- Hebei Normal University of Science and Technology China (People's Republic of)
- Yanshan University China (People's Republic of)
Error bounds for initial value and initial-boundary value problems involving PDEs, Variational methods applied to PDEs, virtual element method, Sobolev equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, error bounds, stability and convergence, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, polygonal meshes, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
Error bounds for initial value and initial-boundary value problems involving PDEs, Variational methods applied to PDEs, virtual element method, Sobolev equations, Finite difference methods for initial value and initial-boundary value problems involving PDEs, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, error bounds, stability and convergence, Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, polygonal meshes, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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