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Regularity and multigrid analysis for Laplace-type axisymmetric equations

Author: Hengguang Li
Journal: Math. Comp. 84 (2015), 1113-1144
MSC (2010): Primary 65N30, 65N55; Secondary 35J05
Published electronically: September 8, 2014
MathSciNet review: 3315502
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Abstract: Consider axisymmetric equations associated with Laplace-type operators. We establish full regularity estimates in high-order Kondrat$ '$ve-type spaces for possible singular solutions due to the non-smoothness of the domain and to the singular coefficients in the operator. Then, we show suitable graded meshes can be used in high-order finite element methods to achieve the optimal convergence rate, even when the solution is singular. Using these results, we further propose multigrid V-cycle algorithms solving the system from linear finite element discretizations on optimal graded meshes. We prove the multigrid algorithm is a contraction, with the contraction number independent of the mesh level. Numerical tests are provided to verify the theorem.

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Additional Information

Hengguang Li
Affiliation: Department of Mathematics, Wayne State University, Detroit, Michigan 48202

Received by editor(s): February 13, 2013
Received by editor(s) in revised form: August 28, 2013
Published electronically: September 8, 2014
Additional Notes: The author was supported in part by the NSF grant DMS-1158839.
Article copyright: © Copyright 2014 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.