Quasi-Optimal Convergence Rate of an Adaptive Discontinuous Galerkin Method
SIAM Journal on Numerical Analysis
Refinement and Connectivity Algorithms for Adaptive Discontinuous Galerkin Methods
SIAM Journal on Scientific Computing
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In this article we present a multilevel preconditioner for interior penalty discontinuous Galerkin discretizations of second order elliptic boundary value problems that gives rise to uniformly bounded condition numbers without any additional regularity assumptions on the solution. The underlying triangulations are assumed only to be shape regular but may have hanging nodes subject to certain mild grading conditions. A key role is played by certain decompositions of the discontinuous trial space into a conforming subspace and a nonconforming subspace that is controlled by the jumps across the edges.