hp-VERSION DISCONTINUOUS GALERKIN FINITE ELEMENT METHOD FOR SEMILINEAR PARABOLIC PROBLEMS

摘要

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.