×

zbMATH — the first resource for mathematics

Robust exponential convergence of the \(hp\) discontinuous Galerkin FEM for convection-diffusion problems in one space dimension. (English) Zbl 0958.65090
This paper deals with the convergence properties of the \(hp\) discontinuous Galerkin finite element method (FEM) for steady advection-diffusion equations in one space dimension. The authors establish robust exponential convergence of the \(hp\) discontinuous Galerkin (DG) FEM without stabilization, and with strong enforcement of the essential boundary conditions, provided the FE-mesh is judiciously chosen. Numerical experiments which confirm this robust exponential convergence of the \(hp\)-DG-FEM are presented.

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
PDF BibTeX XML Cite