$hp$-Version Discontinuous Galerkin Finite Element Method for Semilinear Parabolic Problems

Authors:
Andris Lasis;Endre Süli
Affiliations:
-;-
Venue:
SIAM Journal on Numerical Analysis
Year:
2007

Citing 0
Cited 2

Two-grid finite volume element methods for semilinear parabolic problems

Applied Numerical Mathematics
Local Jacobi Operators and Applications to the $p$-Version of Finite Element Method in Two Dimensions

SIAM Journal on Numerical Analysis

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Abstract

We consider the $hp$-version discontinuous Galerkin finite element method ($hp$-DGFEM) with interior penalty for semilinear parabolic equations with locally Lipschitz continuous nonlinearity, subject to mixed nonhomogeneous Dirichlet-nonhomogeneous Neumann boundary conditions. Our main concern is the error analysis of the (spatially) semidiscrete $hp$-DGFEM on shape-regular spatial meshes. We derive error bounds under various hypotheses on the regularity of the solution, for both the symmetric and nonsymmetric versions of DGFEM.