MooNMD - A program package based on mapped finite element methods

被引：124

作者：

John, Volker ^{[1
]}

Matthies, Gunar ^{[2
]}

机构：

[1] Otto-von-Guericke-Universität Magdeburg, Institut für Analysis und Numerik, 39016 Magdeburg

[2] Ruhr-Universität Bochum, Fakultät für Mathematik, 44780 Bochum

来源：

Computing and Visualization in Science | 2004年 / 6卷 / 2-3期

关键词：

Acknowledgements. The second author was partly supported Deutsche Forschungsgemeinschaft under Grant FOR 301;

D O I：

10.1007/s00791-003-0120-1

中图分类号：

学科分类号：

摘要：

The basis of mapped finite element methods are reference elements where the components of a local finite element are defined. The local finite element on an arbitrary mesh cell will be given by a map from the reference mesh cell. This paper describes some concepts of the implementation of mapped finite element methods. From the definition of mapped finite elements, only local degrees of freedom are available. These local degrees of freedom have to be assigned to the global degrees of freedom which define the finite element space. We will present an algorithm which computes this assignment. The second part of the paper shows examples of algorithms which are implemented with the help of mapped finite elements. In particular, we explain how the evaluation of integrals and the transfer between arbitrary finite element spaces can be implemented easily and computed efficiently. © Springer-Verlag 2004.

引用

页码：163 / 170

页数：7

共 20 条

[1]

Bastian P., Birken K., Johannsen K., Lang S., Neuss N., Rentz-Reichert H., Wieners C., Ug -A flexible software toolbox for solving partial differential equations, Comput. Visual. Sci., 1, pp. 27-40, (1997)

[2]

Behns V., Mortar-Techniken zur Behandlung von Grenzschichtproblemen., (2001)

[3]

Boffi D., Gastaldi L., On the quadrilateral q2-p1 element for the stokes problem, Int. J. Num. Meth. Fluids, 39, 11, pp. 1001-1011, (2002)

[4]

Brenner S.C., Scott L.R., The Mathematical Theory of Finite Element Methods., 15, (1994)

[5]

Ciarlet P.G., Basic error estimates for elliptic problems, Handbook of Numerical Analysis II, pp. 19-351, (1991)

[6]

Dunca A., John V., Layton W.J., Approximating local averages of fluid velocities: The equilibrium navier-stokes equations, Appl. Numer. Math., (2003)

[7]

Girault V., Raviart P.-A., Finite Element Methods for Navier-Stokes Equations., (1986)

[8]

Iliescu T., John V., Layton W.J., Matthies G., Tobiska L., A numerical study of a class of les models, Int. J. Comput. Fluid Dyn., 17, 1, pp. 75-85, (2003)

[9]

John V., Reference values for drag and lift of a two-dimensional time dependent flow around a cylinder, Int. J. Num. Meth. Fluids

[10]

John V., Higher order finite element methods and multigrid solvers in a benchmark problem for the 3D navier-stokes equations, Int. J. Num. Meth. Fluids, 40, pp. 775-798, (2002)

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