A Relation between the Discontinuous Petrov--Galerkin Method and the Discontinuous Galerkin Method
نویسندگان
چکیده
This paper is an attempt in seeking a connection between the discontinuous Petrov– Galerkin method of Demkowicz and Gopalakrishnan [13,15] and the popular discontinuous Galerkin method. Starting from a discontinuous Petrov–Galerkin (DPG) method with zero enriched order we re-derive a large class of discontinuous Galerkin (DG) methods for first order hyperbolic and elliptic equations. The first implication of this result is that the DG method can be considered as the least accurate DPG method. The second implication is that the DPG method can be viewed as a systematic way to improve the accuracy of the DG method when nonzero enriched orders are employed. A detailed derivation of the upwind DG, the local DG, and the hybridized DG from a DPG method with optimal test norms will be presented.
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