hp-Version discontinuous Galerkin finite element methods for semilinear parabolic problems

We consider the hp-version interior penalty discontinuous Galerkin finite element method (hp-DGFEM) for semilinear parabolic equations with mixed Dirichlet and Neumann boundary conditions. Our main concern is the error analysis of the 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 non--symmetric versions of DGFEM

Poincaré-type inequalities for broken Sobolev spaces

We present two versions of general Poincaré-type inequalities for functions in broken Sobolev spaces, providing bounds for the Lq-norm of a function in terms of its broken H1-norm

hp-version discontinuous Galerkin finite element methods for nonlinear parabolic problems

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