hp-Version Discontinuous Galerkin Finite Element Method 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 ...Expand abstract
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