A discontinuous \(hp\) finite element method for diffusion problems: 1-D analysis. (English) Zbl 0940.65076
The mathematical background for a new type of discontinuous Galerkin method is reported, including stability analysis and error estimates, and is illustrated by the numerical analysis of a steady state 1-D diffusion problem. The shape functions are discontinuous at the element boundaries. The main features of the method are: auxiliary variables are not needed; robustness; the method yields elementwise conservative approximations; resulting matrices are positive-definite, well conditioned and convenient for the treatment of transient problems; adaptive error control; acceptable costs.
Reviewer: Nikolai L.Vulchanov (Warszawa)
MSC:
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 34B05 | Linear boundary value problems for ordinary differential equations |
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 65L70 | Error bounds for numerical methods for ordinary differential equations |
Keywords:
discontinuous \(hp\) finite element method; stability; error analysis; 1-D steady state diffusion equation; discontinuous Galerkin methodReferences:
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