an:02082259
Zbl 1059.65095
Wihler, Thomas P.; Frauenfelder, Philipp; Schwab, Christoph
Exponential convergence of the \(hp\)-DGFEM for diffusion problems
EN
Comput. Math. Appl. 46, No. 1, 183-205 (2003).
00098687
2003
j
65N12 65N30 65N50 35J25
FEM; discontinuous Galerkin methods; exponential convergence; diffusion problems; corner singularities; finite element method; mesh refinement; interior penalization; numerical experiments; stabilization
Two different formulations of the \(hp\)-discontinuous Galerkin finite element method (DGFEM) are considered for the two-dimensional stationary diffusion problem. As in the usual FEM, mesh refinement strategy is important when corner singularity caused by polygonal shape of domains exists. The authors prove exponential convergence of the \(hp\)-version of DGFEM on geometrically refined meshes in polygons. Several variants of interior penalization are covered. Numerical experiments indicate the sharpness of the theoretical results as well as the weak dependence of the DGFEM approximation on the particular choice of interior penalization and the penalty parameter. In certain cases, stabilization techniques are effective.
Fumio Kikuchi (Tokyo)