Influence of higher interpolation orders in mixed LSFEM for the incompressible Navier‐Stokes equations

Serdas, Serdar; Schwarz, Alexander; Schröder, Jörg; Turek, Stefan; Ouazzi, Abderrahim; Nickaeen, Masoud

doi:10.1002/pamm.201310146

Cited by 2 publications

(1 citation statement)

References 6 publications

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“…where we have used some additional physically motivated weights on the first and second residual, see e.g. Schwarz and Schröder [2011] and Serdas et al [2013]. The required variation of the functional is explicitly given by…”

Section: Stress-velocity-pressure Formulationmentioning

confidence: 99%

A comparative study of mixed least-squares FEMs for the incompressible Navier-Stokes equations

Schwarz

Nickaeen

Serdas

et al. 2016

IJCSE

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In the present contribution we compare different mixed least-squares finite element formulations (LSFEMs) with respect to computational costs and accuracy. In detail, we consider an approach for Newtonian fluid flow, which is described by the incompressible Navier-Stokes equations. Starting from the residual forms of the equilibrium equation and the continuity condition, various first-order systems are derived. From these systems least-squares functionals are constructed by means of L 2-norms, which are the basis for the associated minimization problems. The first formulation under consideration is a div-grad first-order system resulting in a threefield formulation with stresses, velocities, and pressure as unknowns. This S-V-P formulation is approximated in H(div) × H 1 × L 2 on triangles and for comparison also in H 1 × H 1 × L 2 on quadrilaterals. The second formulation is the well-known div-curl-grad first-order velocityvorticity-pressure (V-V-P) formulation. Here all unknowns are approximated in H 1 on quadrilaterals. Besides some numerical advantages, as e.g. an inherent symmetric structure of the system of equations and a directly available error estimator, it is known that least-squares methods have also a drawback concerning mass conservation, especially when lower-order elements are used. Therefore, the main focus of the work is on performance and accuracy aspects on the one side for finite elements with different interpolation orders and on the other side on the usage of efficient solvers, for instance of Krylov-space or multigrid type. In order to demonstrate the capability of the formulations the results for some well-known benchmark problems are presented and discussed.

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Section: Stress-velocity-pressure Formulationmentioning

confidence: 99%

A comparative study of mixed least-squares FEMs for the incompressible Navier-Stokes equations

Schwarz

Nickaeen

Serdas

et al. 2016

IJCSE

Self Cite

View full text Add to dashboard Cite

show abstract

Least‐squares finite element methods for the Navier‐Stokes equations for generalized Newtonian fluids

Serdas

Schwarz

Schröder

et al. 2014

Proc Appl Math and Mech

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In this contribution we present the least-squares finite element method (LSFEM) for the incompressible Navier-Stokes equations. In detail, we consider a non-Newtonian fluid flow, which is described by a power-law model, see [1]. The second-order problem is reformulated by introducing a first-order div-grad system consisting of the equilibrium condition, the incompressibility condition and the constitutive equation, which are written in residual forms, see [2]. Here, higher-order finite elements which are an important aspect regarding accuracy for the present formulation are investigated.

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Influence of higher interpolation orders in mixed LSFEM for the incompressible Navier‐Stokes equations

Cited by 2 publications

References 6 publications

A comparative study of mixed least-squares FEMs for the incompressible Navier-Stokes equations

A comparative study of mixed least-squares FEMs for the incompressible Navier-Stokes equations

Least‐squares finite element methods for the Navier‐Stokes equations for generalized Newtonian fluids

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