HP -VERSION DISCONTINUOUS GALERKIN FINITE ELEMENT METHODS FOR SEMILINEAR PARABOLIC PROBLEMS

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.

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