Stable splitting of polyharmonic operators by generalized Stokes systems

Dietmar Gallistl

doi:10.1090/mcom/3208

Stable splitting of polyharmonic operators by generalized Stokes systems

Dietmar Gallistl

Research output: Contribution to journal › Article › Academic › peer-review

23 Citations (Scopus)

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≥2 and any integer m≥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.

Original language	English
Pages (from-to)	2555-2577
Number of pages	23
Journal	Mathematics of computation
Volume	86
DOIs	https://doi.org/10.1090/mcom/3208
Publication status	Published - 2017
Externally published	Yes

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10.1090/mcom/3208

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AB - 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≥2 and any integer m≥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.

KW - n/a OA procedure

U2 - 10.1090/mcom/3208

DO - 10.1090/mcom/3208

M3 - Article

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VL - 86

SP - 2555

EP - 2577

JO - Mathematics of computation

JF - Mathematics of computation

ER -

Stable splitting of polyharmonic operators by generalized Stokes systems

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