5,223 research outputs found
A general framework for constructing and analyzing mixed finite volume methods on quadrilateral grids: The overlapping covolume case
No full textWe present a general framework for constructing and analyzing finite volume methods applied to the mixed formulation of second-order elliptic problems on quadrilateral grids. The control volumes, or covolumes, in the grids overlap. An overlapping finite volume method of this type was first introduced by Russell in [T. F. Russell, Tech. report 3, Reservoir Simulation Research Corp., Tulsa, OK, 1995] and was tested for a variety of problems on rectangular and quadrilateral grids in [Z. Cai et al., Comput Geosci., 1 (1997), pp. 289-315]. Later in [S. H. Chou and D. Y. Kwak, SIAM J. Numer. Anal., 37 (2000), pp. 758-771], Chou and Kwak reformulated it as their mixed covolume method and proved optimal order error estimates using the covolume methodology from [S. H. Chou, Math. Comp., 66 (1997), pp. 85-104] and [S. H. Chou and D. Y. Kwak, SIAM J. Numer. Anal., 35 (1998), pp. 494-507]. However, their treatment was restricted to the case of diagonal coefficient tensor and rectangular grids since a different approach was needed for the quadrilateral (distorted rectangular) case. In this paper we give a new framework, which can handle not only the rectangular anisotropic case but also the anisotropic and irregular grid cases in which the locally supported test functions are images of the natural unit coordinate vectors under the Piola transformation. Our theory sheds light on how to create new test functions using quadratures and now covers Russell's quadrilateral case
L-P error estimates and superconvergence for covolume or finite volume element methods
No full textWe consider convergence of the covolume or finite volume element solution to linear elliptic and parabolic problems. Error estimates and superconvergence results in the L-p norm, 2 less than or equal to p less than or equal to infinity, are derived. We also show second-order convergence in the L-p norm between the covolume and the corresponding finite element solutions and between their gradients. The main tools used in this article are an extension of the "supercloseness" results in Chou and Li [Math Comp 69(229) (2000), 103-120] to the L-p based spaces, duality arguments, and the discrete Green's function method. (C) 2003 Wiley Periodicals, Inc
Multigrid algorithms for a vertex-centered covolume method for elliptic problems
No full textWe analyze V-cycle multigrid algorithms for a class of perturbed problems whose perturbation in the bilinear form preserves the convergence properties of the multigrid algorithm of the original problem. As an application, we study the convergence of multigrid algorithms for a covolume method or a vertex-centered finite volume element method for variable coefficient elliptic problems on polygonal domains. As in standard finite element methods, the V-cycle algorithm with one pre-smoothing converges with a rate independent of the number of levels. Various types of smoothers including point or line Jacobi, and Gauss-Seidel relaxation are considered
Characteristic-mixed covolume methods for advection-dominated diffusion problems
No full textCharacteristic-mixed covolume methods for time-dependent advection-dominated diffusion problems are developed and studied. The diffusion term in these problems is discretized using covolume methods applied to the mixed formulation of the problems on quadrilaterals, and the temporal differentiation and advection terms are treated by characteristic tracking schemes. Three characteristic tracking schemes are studied in the context of mixed covolume methods: the modified method of characteristics, the modified method of characteristics with adjusted advection, and the Eulerian-Lagrangian localized adjoint method. The proposed methods preserve the conceptual and computational merits of both characteristics-based schemes and the mixed covolume methods. Existence and uniqueness of a solution to the discrete problem arising from the methods is shown. Stability and convergence properties of these methods are also obtained; unconditionally stable results and error estimates of optimal order are established. Copyright (C) 2006 John Wiley & Sons, Ltd
The pathological study of calves with the Tai-Ta No. 1 centrifugal pump as left ventricular assist device (LVAD)
No full text
Mechanical and electrophysiological effects of 8-oxoberberine (JKL1073A) on atrial tissue.
No full textWellesly Sh. W. to Mr. James Meredith (2 October 1962)
Full text linkSigned by Wellesly Sh. W.https://egrove.olemiss.edu/mercorr_pro/1531/thumbnail.jp
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