hp-DGFEM for Partial Differential Equations with Nonnegative Characteristic Form
We develop the error analysis for the hp-version of a discontinuous finite element approximation to second-order partial differential equations with non-negative characteristic form. This class of equations includes classical examples of second-order elliptic and parabolic equations, first-order hyperbolic equations, as well as equations of mixed type. We establish an a priori error bound for the method which is of optimal order in the mesh size h and 1 order less than optimal in the polynomial degree p. In the particular case of a first-order hyperbolic equation the error bound is optimal in h and 1/2 an order less than optimal in p.
KeywordsFinite Element Method Discontinuous Galerkin Method Finite Element Space Interior Penalty Local Discontinuous Galerkin Method
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