Lumped mass finite element method for hyperbolic equation on rectangular mesh. (Chinese. English summary) Zbl 1270.65059
Summary: The lumped mass finite element method for a hyperbolic equation is discussed on rectangular meshes. Firistly, we study the Crank-Nicolson full-discrete approximation scheme of the lumped mass finite element method for the discussed problem. Secondly, error analysis between the solution of the discussed problem and the solution of the approximated scheme are considered. Without using the traditional elliptic projection operator, the optimal error estimations are obtained on anisotropic meshes.
MSC:
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35L20 | Initial-boundary value problems for second-order hyperbolic equations |
| 65M15 | Error bounds for initial value and initial-boundary value problems involving PDEs |
| 65M50 | Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs |
