Time discretization of parabolic problems by the discontinuous Galerkin method

Discontinuous Galerkin finite element method for parabolic problems

In this paper, we develop a time and its corresponding spatial discretization scheme, based upon the assumption of a certain weak singularity of IIut(t)llLz(n) = llut112, for the discontinuous Galerkin finite element method for one-dimensional parabolic problems. Optimal convergence rates in both time and spatial variables are obtained. A discussion of automatic time-step control method is also...

Bubble stabilized discontinuous Galerkin method for parabolic and elliptic problems

In this paper we give an analysis of a bubble stabilized discontinuous Galerkin method (BSDG) for elliptic and parabolic problems. The method consists of stabilizing the numerical scheme by enriching the discontinuous finite element space elementwise by quadratic non-conforming bubbles. This approach leads to optimal convergence in the space and time discretization parameters. Moreover the dive...

hp Discontinuous Galerkin Time Stepping For Parabolic Problems

The algorithmic pattern of the hp Discontinuous Galerkin Finite Element Method (DGFEM) for the time semidiscretization of abstract parabolic evolution equations is presented. In combination with a continuous hp discretization in space we obtain a fully discrete hp-scheme for the numerical solution of parabolic problems. Numerical examples for the heat equation in a two dimensional domain confir...

BDDC methods for discontinuous Galerkin discretization of elliptic problems

A discontinuous Galerkin (DG) discretization of Dirichlet problem for second-order elliptic equations with discontinuous coefficients in 2-D is considered. For this discretization, balancing domain decomposition with constraints (BDDC) algorithms are designed and analyzed as an additive Schwarz method (ASM). The coarse and local problems are defined using special partitions of unity and edge co...

A-stable discontinuous Galerkin-Petrov time discretization of higher order