Control Volume Finite Difference On Adaptive Meshes

被引：0

作者：

Khattri, Sanjay K. ^{[1
]}

Fladmark, Gunnar E. ^{[1
]}

Dahle, Helge K. ^{[1
]}

机构：

[1] Department of Mathematics, University Bergen

来源：

Lecture Notes in Computational Science and Engineering | 2007年 / 55卷

关键词：

D O I：

10.1007/978-3-540-34469-8_78

中图分类号：

学科分类号：

摘要：

In this work we present a finite volume discretization of an elliptic boundary value problem on adaptively refined meshes. This problem is important in many practical applications, e.g. porous media flow. We propose an error indicator functional which is used to select elements that should be refined. Two numerical examples are provided to demonstrate the potential of the proposed refinement strategy.

引用

页码：627 / 633

页数：6

共 10 条

[1]

Aavatsmark I., An introduction to multipoint flux approximations for quadrilateral grids, Comput. Geosci, 6, pp. 405-432, (2002)

[2]

Babuska I., Miller A., A feedback finite element method with a posteriori error estimation: Part I. The finite element method and some basic properties of the a posteriori error estimators, Comp. Meth. Appl. Mech. Eng, 61, pp. 1-40, (1987)

[3]

Babuska I., Rheinboldt W.C., Analysis of optimal finite element meshes in r<sup>1</sup>, Math. Comp, 33, pp. 435-463, (1979)

[4]

Chen Z., Dai S., On the efficiency of adaptive finite element methods for elliptic problems with discontinuous coefficients, SIAM J. Sci. Comput, 24, pp. 443-462, (2002)

[5]

Edwards M.G., Rogers C.F., Finite volume discretization with imposed flux continuity for the general tensor pressure equation, Comput. Geosci, 2, pp. 259-290, (1998)

[6]

Eigestad G.T., Klausen R.A., On the convergence of the multi-point flux approximation O-method: Numerical experiments for discontinuous permeability, Numer. Methods Partial Differential Equations, 21, pp. 1079-1098, (2005)

[7]

Khattri S.K., Numerical tools for multi-component, multi-phase, reactive transport in porous medium, (2006)

[8]

Morin P., Nochetto R.H., Siebert K.G., Data oscillation and convergence of adaptive FEM, SIAM J. Numer. Anal, 38, pp. 466-488, (2000)

[9]

Riviere B.M., Discontinuous Galerkin Fnite Element Methods for Solving the Miscible Displacement Problem in Porous Media, (2000)

[10]

Strang G., Fix G.J., An Analysis of the Finite Element Method, (1973)

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