Publication Results

Code: 56/2014
Title: A uniform additive Schwarz preconditioner for the hp-version of Discontinuous Galerkin approximations of elliptic problems
Date: Tuesday 2nd December 2014
Author(s) : Antonietti, P. F.; Sarti, M.; Verani, M.; Zikatanov, L. T.
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Abstract: In this paper we design and analyze a uniform preconditioner for a class of high order Discontinuous Galerkin schemes. The preconditioner is based on a space splitting involving the high order conforming subspace and results from the interpretation of the problem as a nearly-singular problem. We show that the proposed preconditioner exhibits spectral bounds that are uniform with respect to the discretization parameters, i.e., the mesh size, the polynomial degree and the penalization coefficient. The theoretical estimates obtained are supported by several numerical simulations.

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IMA Journal of Numerical Analysis