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Stable splitting of polyharmonic operators by generalized Stokes systems


Author: Dietmar Gallistl
Journal: Math. Comp. 86 (2017), 2555-2577
MSC (2010): Primary 31B30, 35J30, 65N12, 65N15, 65N30
DOI: https://doi.org/10.1090/mcom/3208
Published electronically: March 29, 2017
MathSciNet review: 3667017
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Abstract: A stable splitting of $2m$-th order elliptic partial differential equations into $2(m-1)$ problems of Poisson type and one generalized Stokes problem is established for any space dimension $d\geq 2$ and any integer $m\geq 1$. This allows a numerical approximation with standard finite elements that are suited for the Poisson equation and the Stokes system, respectively. For some fourth- and sixth-order problems in two and three space dimensions, precise finite element formulations along with a priori error estimates and numerical experiments are presented.


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Additional Information

Dietmar Gallistl
Affiliation: Institut für Angewandte und Numerische Mathematik, Karlsruher Institut für Technologie, Englerstr. 2, 76131 Karlsruhe, Germany
MR Author ID: 1020312

Keywords: Finite element methods, Stokes system, mixed finite elements, polyharmonic equation
Received by editor(s): January 4, 2016
Received by editor(s) in revised form: July 7, 2016
Published electronically: March 29, 2017
Article copyright: © Copyright 2017 American Mathematical Society