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Main Title: Finite Element Decomposition and Minimal Extension for Flow Equations
Author(s): Altmann, Robert
Heiland, Jan
Type: Research Paper
Abstract: In the simulation of flows, the correct treatment of the pressure variable is the key to stable time-integration schemes. This paper contributes a new approach based on the theory of differential-algebraic equations. Motivated by the index reduction technique of minimal extension, a decomposition of finite element spaces is proposed that ensures stable and accurate approximations. The presented decomposition -- for standard finite element spaces used in CFD -- preserves sparsity and does not call on variable transformations which might change the meaning of the variables. Since the method is eventually an index reduction, high index effects leading to instabilities are eliminated. As a result, all constraints are maintained and one can apply semi-explicit time integration schemes.
Subject(s): Navier-Stokes equations
time integration schemes
finite element method
index reduction
operator DAE
Issue Date: 19-Apr-2013
Date Available: 17-Dec-2021
Language Code: en
DDC Class: 510 Mathematik
MSC 2000: 76M10 Finite element methods
65L80 Methods for differential-algebraic equations
65J10 Equations with linear operators
Series: Preprint-Reihe des Instituts für Mathematik, Technische Universität Berlin
Series Number: 2013, 11
ISSN: 2197-8085
TU Affiliation(s): Fak. 2 Mathematik und Naturwissenschaften » Inst. Mathematik
Appears in Collections:Technische Universität Berlin » Publications

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