Superconvergence properties of discontinuous Galerkin methods for two-point boundary value problems. (English) Zbl 1110.65074
This paper deals with discontinuous Galerkin methods for solving a two-point boundary value problem. The aim is to analyze the superconvergence property. Three types of methods are studied: the symmetric and the non-symmetric interior penalty method, the discontinuous Galerkin method without penalty terms. Numerical experiments support the theoretical results.
Reviewer: Rudolf Scherer (Karlsruhe)
MSC:
| 65L20 | Stability and convergence of numerical methods for ordinary differential equations |
| 65L10 | Numerical solution of boundary value problems involving ordinary differential equations |
| 65L60 | Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations |
| 34B05 | Linear boundary value problems for ordinary differential equations |
