Abstract
Hybrid discontinuous Galerkin methods are popular discretization methods in applications from fluid dynamics and many others. Often large scale linear systems arising from elliptic operators have to be solved. We show that standard p-version domain decomposition techniques can be applied, but we have to develop new technical tools to prove poly-logarithmic condition number estimates, in particular on tetrahedral meshes.
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Keywords
- Elliptic Problem
- Domain Decomposition
- Discontinuous Galerkin
- Discontinuous Galerkin Method
- Extension Operator
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Schöberl, J., Lehrenfeld, C. (2013). Domain Decomposition Preconditioning for High Order Hybrid Discontinuous Galerkin Methods on Tetrahedral Meshes. In: Apel, T., Steinbach, O. (eds) Advanced Finite Element Methods and Applications. Lecture Notes in Applied and Computational Mechanics, vol 66. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30316-6_2
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