A new error analysis for discontinuous finite element methods for linear elliptic problems. (English) Zbl 1201.65198
The authors present a new error analysis for discontinuous finite element methods for linear elliptic problems. They first present the main result in an abstract lemma which enables to decompose the error. Applications of the abstract lemma to various nonconforming and discontinuous Galerkin methods for second and fourth order elliptic problems are given. Possible extensions are presented.
Reviewer: Seenith Sivasundaram (Daytona Beach)
MSC:
| 65N15 | Error bounds for boundary value problems involving PDEs |
| 65N30 | Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs |
| 35J25 | Boundary value problems for second-order elliptic equations |
| 35J40 | Boundary value problems for higher-order elliptic equations |
Keywords:
optimal error estimates; elliptic regularity; finite element method; discontinuous Galerkin method; nonconforming; boundary value problem; linear elliptic problems; second and fourth order elliptic problemsReferences:
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