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An elliptic boundary-value problem on a domain with prescribedDirichlet data on I is approximated using a finite-elementspace of approximation power hK in the L2 norm. It is shownthat the total flux across I can be approximated with an errorof O(hK) when is a curved domain in Rn (n = 2 or 3) and isoparametricelements are used. When is a polyhedron, an O(h2K2)approximation is given. We use these results to study the finite-elementapproximation of elliptic equations when the prescribed boundarydata on I is the total flux.
Present address: School of Mathematical and Physical Sciences,University of Sussex, Brighton, Sussex BN1 9QH. 相似文献
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BARRETT JOHN W.; CHAKRABARTI ROMA; ELLIOTT CHARLES M. 《IMA Journal of Numerical Analysis》1991,11(4):579-594
Optimal order H1 and L error bounds are obtained for a continuouspiecewise linear finite element approximation of an obstacleproblem, where the obstacle's height as well as the contactzone, c, are a priori unknown. The problem models the indentationof a membrane by a rigid punch. For R2, given ,g R+ and an obstacle defined over E we consider the minimization of |v|21,+gµover (v, µ) H10() x R subject to v+µ on E. In additionwe show under certain nondegeneracy conditions that dist (c,hc)Ch ln 1/h, where hc is the finite element approximation toc. Finally we show that the resulting algebraic problem canbe solved using a projected SOR algorithm. 相似文献
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We consider a fully discrete implicit finite-element approximationof a model for the phase separation of a multi-component alloy.We prove existence, uniqueness and stability of the numericalsolution for a sufficiently small time step. We prove convergenceto the solution of the associated continuous problem. We performa linear stability analysis of the equation and describe somenumerical experiments. 相似文献
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A finite difference approximation of the non-linear diffusionequation et = ((e))xx' where is non-monotone, is shown to convergeto a measure valued solution. Some numerical results are described. 相似文献
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An electrochemical machining moving boundary problem is formulated,after a change of variable, as an elliptic variational inequality.The unknown anode surface may now be found by solving just oneelliptic free boundary problem. The variational inequality isapproximated by the finite element method and numerical resultsare presented. 相似文献
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Two algorithms for the approximate evaluation of certain Hadamardfinite-part integrals, which date back to Grünwald (1867),have been analysed. It is shown that the quadrature sums areclosely related to the finite-part integrals of the Bernsteinpolynomials. The stability of the algorithms is considered andtwo numerical examples are given. 相似文献
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This paper considers a finite-element approximation of a Poissonequation in a region with a curved boundary on which a Neumanncondition is prescribed. Piecewise linear and bilinear elementsare used on unfitted meshes with the region of integration beingreplaced by a polygonal approximation. It is shown, despitethe variational crimes, that the rate of convergence is stillorder (h) in the H1 norm. Numerical examples show that the methodis easy to implement and that the predicted rate of convergenceis obtained.
Supported by SERC postdoctoral fellowship RF/5830. 相似文献
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An initial-boundary-value problem for a parabolic equation ina domain x (0, T) with prescribed Dirichlet data on is approximatedusing a continuous-time Galerkin finite-element scheme. It isshown that the total flux across 1= can be approximated withan error of O(hk) when is a curved domain in Rn (n = 2 or 3)and isoparametric elements having approximation power hk inthe L2 norm are used. 相似文献
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Grnwald's algorithms for the numerical evaluation of Hadamardfinite-part integrals with non-integer exponent are extendedto the case of integer exponent. These algorithms are basedon the use of Bernstein polynomials and it is shown how, byan appropriate modification of the first algorithm, a convergencerate of order 1/N2 may be obtained, where N is the number offunction evaluations. 相似文献