Discontinuous Galerkin Methods for Friedrichs' Systems. I. General theory
نویسندگان
چکیده
منابع مشابه
Discontinuous Galerkin methods for Friedrichs’ systems∗
This work presents a unified analysis of Discontinuous Galerkin methods to approximate Friedrichs’ systems. A general set of boundary conditions is identified to guarantee existence and uniqueness of solutions to these systems. A formulation enforcing the boundary conditions weakly is proposed. This formulation is the starting point for the construction of Discontinuous Galerkin methods formula...
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This paper presents a unified analysis of Discontinuous Galerkin methods to approximate Friedrichs' symmetric systems. An abstract set of conditions is identified at the continuous level to guarantee existence and uniqueness of the solution in a subspace of the graph of the differential operator. Then a general Discontinuous Galerkin method that weakly enforces boundary conditions and mildly pe...
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This paper is the second part of a work attempting to give a unified analysis of Discontinuous Galerkin methods. The setting under scrutiny is that of Friedrichs’ systems endowed with a particular 2×2 structure in which some of the unknowns can be eliminated to yield a system of second-order elliptic-like PDE’s for the remaining unknowns. For such systems, a general Discontinuous Galerkin metho...
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This paper is the third and last part of a work attempting to give a unified analysis of Discontinuous Galerkin methods. The purpose of this paper is to extend the framework that has been developed in part II for two-field Friedrichs’ systems associated with second-order PDE’s. We now consider two-field Friedrichs’ systems with partial L2-coercivity and three-field Friedrichs’ systems with an e...
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ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2006
ISSN: 0036-1429,1095-7170
DOI: 10.1137/050624133