hp-Discontinuous Galerkin Finite Element Methods with Least-Squares Stabilization

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【作者】 Houston  Paul  Jensen  Max    li  Endre 


【摘要】We consider a family of hp-version discontinuous Galerkin finite element methods with least-squares stabilization for symmetric systems of first-order partial differential equations. The family includes the classical discontinuous Galerkin finite element method, with and without streamline-diffusion stabilization, as well as the discontinuous version of the Galerkin least-squares finite element method. An hp-optimal error bound is derived in the associated DG-norm. If the solution of the problem is elementwise analytic, an exponential rate of convergence under p-refinement is proved. We perform numerical experiments both to illustrate the theoretical results and to compare the various methods within the family.</p>

【刊名】Journal of Scientific Computing