Discretization schemes of triangular grids
type: Item
instance of: scholarly article
title: Discretization schemes of triangular grids
zbMATH Open document ID: 0943.65120
DOI: 10.1016/S0045-7825(97)00191-6
author: R. Ewing
author: Ove Sævareid
author: J. Shen
published in: Computer Methods in Applied Mechanics and Engineering
publication date: 2000-03-21T00:00:00Z
review text: Physical applications posed on irregular domains have caused difficulties in the use of many, otherwise effective, discretization schemes. In two-dimensional examples, we consider discretization schemes on triangles to approximate irregular domains. Although finite element, mixed finite element, and finite volume schemes for triangles are well understood, efficient solvers are essential for their effective use. In this paper, we consider certain cell-centered finite difference schemes on triangles, both for their theoretical properties on regular grids, and as effective preconditioners for other discretization schemes for more general triangulations. Two cell-centered finite difference schemes (four-point star stencils) are derived from the simplification of the lowest-order Raviart-Thomas mixed finite element discretization on certain triangular grids. Optimal and superconvergence, error estimates for both the solution and the gradient of the solution are established. The accuracy of these schemes is also discussed in the case of discontinuous coefficients. Computational experiments verify the error estimates. Finally, the use of these methods as preconditioners is also discussed.
Mathematics Subject Classification ID: 65N06
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 65N12
Mathematics Subject Classification ID: 65N15
Mathematics Subject Classification ID: 35J25
zbMATH DE Number: 1420327
zbMATH Keywords: computational experiments
zbMATH Keywords: irregular domains
zbMATH Keywords: cell-centered finite difference schemes
zbMATH Keywords: preconditioners
zbMATH Keywords: mixed finite element
zbMATH Keywords: superconvergence
zbMATH Keywords: error estimates
MaRDI profile type: Publication
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full work available at URL: s0045-7825(97)00191-6
OpenAlex ID: W2063192122
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description: scientific article; zbMATH DE number 1420327