hp-version discontinuous Galerkin finite element method for semilinear parabolic problems

摘要

We consider the hp-version discontinuous Galerkin finite element method (hpDGFEM) 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.