Mixed and hybrid finite element methods
Mixed and hybrid finite element methods
Performance of Discontinuous Galerkin Methods for Elliptic PDEs
SIAM Journal on Scientific Computing
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
An A Priori Error Analysis of the Local Discontinuous Galerkin Method for Elliptic Problems
SIAM Journal on Numerical Analysis
Poincaré-Friedrichs Inequalities for Piecewise H1 Functions
SIAM Journal on Numerical Analysis
SIAM Journal on Scientific Computing
Locally Conservative Fluxes for the Continuous Galerkin Method
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
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Based on Cockburn et al. (Math. Comp. 78:1---24, 2009), superconvergent discontinuous Galerkin methods are identified for linear non-selfadjoint and indefinite elliptic problems. With the help of an auxiliary problem which is the discrete version of a linear non-selfadjoint elliptic problem in divergence form, optimal error estimates of order k+1 in L 2-norm for the potential and the flux are derived, when piecewise polynomials of degree k驴1 are used to approximate both potential and flux variables. Using a suitable post-processing of the discrete potential, it is then shown that the resulting post-processed potential converges with order k+2 in L 2-norm. The article is concluded with a numerical experiment which confirms the theoretical results.