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Simulation of Flow in Fractured Poroelastic Media: A Comparison of Different Discretization Approaches Read chapter Read first chapter

2015 | OriginalPaper | Chapter

Some Results of FEM Schemes Analysis by Finite Difference Method

Author : Dmitry T. Chekmarev

Published in: Finite Difference Methods,Theory and Applications

Publisher: Springer International Publishing

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Abstract

A method of investigation of numerical schemes deriving from the variational formulation of the problem (variational- difference method and FEM) is discusses. The method is based on the reduction of the numerical schemes to the canonical finite difference form. The resulting numerical scheme standard notation in the form of a grid operator equality is used for analyzing its approximation, stability and other properties. The application of this approach to a wider classes of finite elements (from the simplest ones to the Hermitian elements and serendipities) is discussed. These opportunities are illustrated by the analysis of FEM schemes for Timoshenko shells and elasticity dynamic problems.

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previous chapter Difference Schemes for Delay Parabolic Equations with Periodic Boundary Conditions
next chapter Application of Finite Difference TVD Methods in Hypersonic Aerodynamics
Literature
1.
Bazhenov, V.G., Chekmarev, D.T.: Solving the problems of plates and shells dynamics by variational- difference method, Nizhny Novgorod (2000) (in Russian)
2.
Bazhenov, V.G., Chekmarev, D.T.: On numerical differentiation index commutation. Comp. Math. and Math. Phys. 29(5), 662–674 (1989). (in Russian)MATHMathSciNet
3.
Zienkiewicz, O.C., Morgan, K.: Finite Elements and Approximation. Wiley, New York (1983)MATH
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Strang, G., Fix, G.J.L: An Analysis of the Finite Element Method. Series in Aut. Comp. pp. XIV + 306 SM Fig. Prentice-Hall Inc, Englewood Clifs, NJ (1973)
5.
Timoshenko, S.: Vibration problems in engineering. Van Nostrand, New York (1937)MATH
6.
Zienkiewich, O.C., Too, J., Taylor, R.L.: Reduced integration technique in general analysis of plates and shells. Int. J. Num. Meth. Engng. 3(2), 275–290 (1971)CrossRef
7.
Chekmarev, D.T.: Finite element schemes on rare meshes. Probl. At. Sci. Techn. Ser. Math. Model. phys. proc. 2, 49–54 (2009). (in Russian)
8.
Zhidkov, A.V., Zefirov, S.V., Kastalkaya, K.A., Spirin, S.V., Chekmarev, D.T.: Rare mesh scheme for numerical solution of three-dimensional dynamic problems of elasticity and plasticity. Bull. Nizhny Novgorod Univ. 4(4), 1480–1485 (2011). (in Russian)
Metadata
Title
Some Results of FEM Schemes Analysis by Finite Difference Method
Author
Dmitry T. Chekmarev
Copyright Year
2015
Book
Finite Difference Methods,Theory and Applications

Print ISBN: 978-3-319-20238-9

Electronic ISBN: 978-3-319-20239-6

Copyright Year: 2015

DOI
https://doi.org/10.1007/978-3-319-20239-6_14

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