Spectral element multigrid. I. Formulation and numerical results
Journal of Scientific Computing
Spectral element multigrid. II. theoretical justification
Journal of Scientific Computing
Iterative solvers by substructuring for the p-version finite element method
ICOSAHOM '89 Proceedings of the conference on Spectral and high order methods for partial differential equations
Efficient preconditioning for the p-version finite element method in two dimensions
SIAM Journal on Numerical Analysis
Multi-p methods: iterative algorithms for the p-version of the finite element analysis
SIAM Journal on Scientific Computing
SIAM Journal on Numerical Analysis
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
Domain decomposition: parallel multilevel methods for elliptic partial differential equations
SIAM Journal on Scientific Computing
Finite Element Method for Elliptic Problems
Finite Element Method for Elliptic Problems
Performance of Discontinuous Galerkin Methods for Elliptic PDEs
SIAM Journal on Scientific Computing
Discontinuous hp-Finite Element Methods for Advection-Diffusion-Reaction Problems
SIAM Journal on Numerical Analysis
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
SIAM Journal on Numerical Analysis
Iterative Methods for Sparse Linear Systems
Iterative Methods for Sparse Linear Systems
Algebraic multigrid for higher-order finite elements
Journal of Computational Physics
deal.II—A general-purpose object-oriented finite element library
ACM Transactions on Mathematical Software (TOMS)
Algebraic Multigrid for Linear Systems Obtained by Explicit Element Reduction
SIAM Journal on Scientific Computing
Time Implicit High-Order Discontinuous Galerkin Method with Reduced Evaluation Cost
SIAM Journal on Scientific Computing
Journal of Computational Physics
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We derive and analyze a block diagonal preconditioner for the linear problems arising from a discontinuous Galerkin finite element discretization. The method can be applied to second-order self-adjoint elliptic boundary value problems and exploits the natural decomposition of the discrete function space into a global low-order subsystem and components of higher polynomial degree. Similar to results for the p-version of the conforming FEM, we prove for the interior penalty discontinuous Galerkin discretization that the condition number of the preconditioned system is uniformly bounded with respect to the mesh size of the triangulation. Numerical experiments demonstrate the performance of the method.