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Contributions to Books:

J. Melenk, H. Rezaijafari, B. Wohlmuth:
"Quasi-optimal a priori estimates for fluxes in mixed finite element methods and applications to the Stokes-Darcy coupling";
in: "ASC Report 05/2012", issued by: Institute for Analysis and Scientific Computing; Vienna University of Technology, Wien, 2012, ISBN: 978-3-902627-05-6, 1 - 23.

English abstract:
We show quasi-optimal a priori convergence results in the $L^2$-norm on interfaces for the approximation of the normal component of the flux in mixed finite element methods.
Compared to standard estimates for this problem class, an additional factor $\sqrt{h} | \log h |$ in the {\sl a priori} bound for the flux variable is obtained by using new upper estimates in strips of width $O(h)$ near these interfaces. An important role in the analysis play anisotropic and weighted norms. Numerical results including an application to the Darcy--Stokes coupling illustrate our theoretical results.

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

Electronic version of the publication:

Created from the Publication Database of the Vienna University of Technology.