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Uniform Stability and Error Analysis for Some Discontinuous Galerkin Methods
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In this paper, we provide a number of new estimates on the stability and convergence of both hybrid discontinuous Galerkin (HDG) and weak Galerkin (WG) methods. By using the standard Brezzi theory on mixed methods, we carefully define appropriate norms for the various discretization variables and then establish that the stability and error estimates hold uniformly with respect to stabilization and discretization parameters. As a result, by taking appropriate limit of the stabilization parameters, we show that the HDG method converges to a primal conforming method and the WG method converge to a mixed conforming method.
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An Extended Galerkin Analysis for Elliptic Problems
A four-field Galerkin formulation with two boundary trace corrections is introduced, and two parameter-uniform inf-sup theorems are proved that recover and analyze many existing finite element, discontinuous Galerkin,...
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