Improved energy estimates for interior penalty, constrained and discontinuous Galerkin methods for elliptic problems. I
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.
non-symmetric interior penalty Galerkin method
non-symmetric constrained Galerkin method
scientific article; zbMATH DE number 1456881