Abstract
We identify and study an LDG-hybridizable Galerkin method, which is not an LDG method, for second-order elliptic problems in several space dimensions with remarkable convergence properties. Unlike all other known discontinuous Galerkin methods using polynomials of degree k ≧ 0 for both the potential as well as the flux, the order of convergence in L2 of both unknowns is k + 1. Moreover, both the approximate potential as well as its numerical trace superconverge in L2-like norms, to suitably chosen projections of the potential, with order k + 2. This allows the application of element-by-element postprocessing of the approximate solution which provides an approximation of the potential converging with order K + 2 in L2. The method can be thought to be in between the hybridized version of the Raviart-Thomas and that of the Brezzi-Douglas-Marini mixed methods.
Original language | English (US) |
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Pages (from-to) | 1887-1916 |
Number of pages | 30 |
Journal | Mathematics of Computation |
Volume | 77 |
Issue number | 264 |
DOIs | |
State | Published - Oct 2008 |
Keywords
- Discontinuous Galerkin methods
- Hybridization
- Second-order elliptic problems
- Superconvergence