Displaying similar documents to “Discretisation and error estimates for elliptic boundary value problems of the fourth order”

Penalty method and extrapolation for axisymmetric elliptic problems with Dirichlet boundary conditions

Ivan Hlaváček (1990)

Aplikace matematiky

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A second order elliptic problem with axisymmetric data is solved in a finite element space, constructed on a triangulation with curved triangles, in such a way, that the (nonhomogeneous) boundary condition is fulfilled in the sense of a penalty. On the basis of two approximate solutions, extrapolates for both the solution and the boundary flux are defined. Some a priori error estimates are derived, provided the exact solution is regular enough. The paper extends some of the results of...

On the efficient use of the Galerkin-method to solve Fredholm integral equations

Wolfgang Hackbusch, Stefan A. Sauter (1993)

Applications of Mathematics

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In the present paper we describe, how to use the Galerkin-method efficiently in solving boundary integral equations. In the first part we show how the elements of the system matrix can be computed in a reasonable time by using suitable coordinate transformations. These techniques can be applied to a wide class of integral equations (including hypersingular kernels) on piecewise smooth surfaces in 3-D, approximated by spline functions of arbitrary degree. In the second part we show, how...

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...