Abstract
For classical discretizations of elliptic partial differential equations, like conforming finite elements or finite differences, block Jacobi methods are equivalent to classical Schwarz methods with Dirichlet transmission conditions. This is however not necessarily the case for discontinuous Galerkin methods (DG). We will show for the model problem \(-\varDelta u = f\) and various DG discretizations that a block Jacobi method applied to the discretized problem can be interpreted as a Schwarz method with different transmission conditions.
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Acknowledgements
We would like to thank BLANCA AYUSO for her useful comments.
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© 2014 Springer International Publishing Switzerland
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Gander, M.J., Hajian, S. (2014). Block Jacobi for Discontinuous Galerkin Discretizations: No Ordinary Schwarz Methods. In: Erhel, J., Gander, M., Halpern, L., Pichot, G., Sassi, T., Widlund, O. (eds) Domain Decomposition Methods in Science and Engineering XXI. Lecture Notes in Computational Science and Engineering, vol 98. Springer, Cham. https://doi.org/10.1007/978-3-319-05789-7_27
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DOI: https://doi.org/10.1007/978-3-319-05789-7_27
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