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

Journal article

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. © 2007 Society for Industrial and Applied Mathematics.

Authors: Lasis, A; Süli, E

• Publication status: Published
• Journal: SIAM J. Numerical Analysis
• Volume: 45
• Issue: 4
• Pages: 1544-1569
• Publication date: 2007-01-01
• DOI: 10.1137/050642125
• EISSN: 1095-7170
• ISSN: 0036-1429
• Language: English
• Keywords: discontinuous Galerkin methods; semilinear parabolic PDEs; hp-finite element methods