A Uniform Additive Schwarz Preconditioner for High-Order Discontinuous Galerkin Approximations of Elliptic Problems

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• 作者：Paola F. Antonietti ; Marco Sarti ; Marco Verani…
• 关键词：Discontinuous Galerkin method ; High ; order discretizations ; Uniform preconditioning
• 刊名：Journal of Scientific Computing
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：70
• 期：2
• 页码：608-630
• 全文大小：
• 刊物类别：Mathematics and Statistics
• 刊物主题：Algorithms; Computational Mathematics and Numerical Analysis; Appl.Mathematics/Computational Methods of Engineering; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer US
• ISSN：1573-7691
• 卷排序：70

文摘

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 numerical tests.