New finite element method for solving a wave equation with a nonlocal conservation condition. (English) Zbl 1302.82007
Summary: A wave equation with a nonlocal boundary condition is considered. Then we purpose a new finite element method for solving this equation. Also, we obtain a priori and a posteriori error estimates. The theory is illustrated by some numerical examples.
MSC:
| 82-08 | Computational methods (statistical mechanics) (MSC2010) |
| 35L05 | Wave equation |
| 65M60 | Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs |
| 35B45 | A priori estimates in context of PDEs |
| 65F10 | Iterative numerical methods for linear systems |
Keywords:
hyperbolic problems; nonlocal boundary condition; wave equations; finite element; error estimateReferences:
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