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Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I. (English) Zbl 0951.65108
The authors discuss three numerical algorithms for elliptic problems which employ discontinuous approximation spaces and obtain optimal a priori \(hp\) error estimates in \(H^1\) and \(L^2\) or \(H^1\) for all three procedures. The three methods are called the non-symmetric interior penalty Galerkin method, the non-symmetric constrained Galerkin method, and the discontinuous Galerkin method. The three algorithms are closely related in that the underlying bilinear form for all three is the same and is non-symmetric. All three methods are locally conservative.

65N15 Error bounds for boundary value problems involving PDEs
65N30 Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
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