Displaying similar documents to “Some fast finite-difference solvers for Dirichlet problems on general domains”

On multi-parameter error expansions in finite difference methods for linear Dirichlet problems

Ta Van Dinh (1987)

Aplikace matematiky

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The paper is concerned with the finite difference approximation of the Dirichlet problem for a second order elliptic partial differential equation in an n -dimensional domain. Considering the simplest finite difference scheme and assuming a sufficient smoothness of the domain, coefficients of the equation, right-hand part, and boundary condition, the author develops a general error expansion formula in which the mesh sizes of an ( n -dimensional) rectangular grid in the directions of the...

A new finite element approach for problems containing small geometric details

Wolfgang Hackbusch, Stefan A. Sauter (1998)

Archivum Mathematicum

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In this paper a new finite element approach is presented which allows the discretization of PDEs on domains containing small micro-structures with extremely few degrees of freedom. The applications of these so-called Composite Finite Elements are two-fold. They allow the efficient use of multi-grid methods to problems on complicated domains where, otherwise, it is not possible to obtain very coarse discretizations with standard finite elements. Furthermore, they provide a tool for discrete...