Quasi-optimal a priori estimates for fluxes in mixed finite element methods and an application to the Stokes-Darcy coupling

J. M. Melenk; H. Rezaijafari; B. Wohlmuth

doi:10.1093/imanum/drs048

Quasi-optimal a priori estimates for fluxes in mixed finite element methods and an application to the Stokes-Darcy coupling

J. M. Melenk, H. Rezaijafari, B. Wohlmuth

Chair of Numerical Analysis

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

11 Scopus citations

Abstract

We show improved a priori convergence results in the L² norm on interfaces for the approximation of the normal component of the flux in mixed finite element methods. Compared with standard estimates for this problem class, additional factors of for the lowest-order case and of in the higher-order case in the a priori bound for the flux variable are obtained. An important role in the analysis play new error estimates in strips of width (h) and the use of anisotropic and weighted norms. Numerical examples including an application to the Stokes-Darcy coupling illustrate our theoretical results.

Original language	English
Pages (from-to)	1-27
Number of pages	27
Journal	IMA Journal of Numerical Analysis
Volume	34
Issue number	1
DOIs	https://doi.org/10.1093/imanum/drs048
State	Published - Jan 2014

Keywords

Stokes-Darcy coupling
anisotropic norms
local FEM error analysis
mixed finite elements
saddle point problem
weighted norms

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10.1093/imanum/drs048

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title = "Quasi-optimal a priori estimates for fluxes in mixed finite element methods and an application to the Stokes-Darcy coupling",

abstract = "We show improved a priori convergence results in the L2 norm on interfaces for the approximation of the normal component of the flux in mixed finite element methods. Compared with standard estimates for this problem class, additional factors of for the lowest-order case and of in the higher-order case in the a priori bound for the flux variable are obtained. An important role in the analysis play new error estimates in strips of width (h) and the use of anisotropic and weighted norms. Numerical examples including an application to the Stokes-Darcy coupling illustrate our theoretical results.",

keywords = "Stokes-Darcy coupling, anisotropic norms, local FEM error analysis, mixed finite elements, saddle point problem, weighted norms",

author = "Melenk, {J. M.} and H. Rezaijafari and B. Wohlmuth",

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AU - Melenk, J. M.

AU - Rezaijafari, H.

AU - Wohlmuth, B.

N1 - Funding Information: The research was carried out while J.M.M. and B.W. attended the ‘special semester’ on ‘Multiscale Simulation & Analysis in Energy and the Environment’ hosted by the Johann Radon Institute for Computational and Applied Mathematics (RICAM) in Linz, 3 October 2011–15 December 2011. The hospitality and financial support of the RICAM is very gratefully acknowledged.

PY - 2014/1

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N2 - We show improved a priori convergence results in the L2 norm on interfaces for the approximation of the normal component of the flux in mixed finite element methods. Compared with standard estimates for this problem class, additional factors of for the lowest-order case and of in the higher-order case in the a priori bound for the flux variable are obtained. An important role in the analysis play new error estimates in strips of width (h) and the use of anisotropic and weighted norms. Numerical examples including an application to the Stokes-Darcy coupling illustrate our theoretical results.

AB - We show improved a priori convergence results in the L2 norm on interfaces for the approximation of the normal component of the flux in mixed finite element methods. Compared with standard estimates for this problem class, additional factors of for the lowest-order case and of in the higher-order case in the a priori bound for the flux variable are obtained. An important role in the analysis play new error estimates in strips of width (h) and the use of anisotropic and weighted norms. Numerical examples including an application to the Stokes-Darcy coupling illustrate our theoretical results.

KW - Stokes-Darcy coupling

KW - anisotropic norms

KW - local FEM error analysis

KW - mixed finite elements

KW - saddle point problem

KW - weighted norms

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DO - 10.1093/imanum/drs048

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JO - IMA Journal of Numerical Analysis

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ER -

Quasi-optimal a priori estimates for fluxes in mixed finite element methods and an application to the Stokes-Darcy coupling

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Keywords

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