Enclosures and semi-analytic discretization of boundary value problems
c. Grossmann (1994)
Banach Center Publications
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c. Grossmann (1994)
Banach Center Publications
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Josef Dalík (1991)
Applications of Mathematics
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A general construction of test functions in the Petrov-Galerkin method is described. Using this construction; algorithms for an approximate solution of the Dirichlet problem for the differential equation are presented and analyzed theoretically. The positive number is supposed to be much less than the discretization step and the values of . An algorithm for the corresponding two-dimensional problem is also suggested and results of numerical tests are introduced.
Roos, Hans-Görg, Zarin, Helena (2003)
Novi Sad Journal of Mathematics
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Eric Boillat (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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The present paper deals with a finite element approximation of partial differential equations when the domain is decomposed into sub-domains which are meshed independently. The method we obtain is never conforming because the continuity constraints on the boundary of the sub-domains are not imposed strongly but only penalized. We derive a selection rule for the penalty parameter which ensures a quasi-optimal convergence.
Knabner, P., Tapp, C., Thiele, K. (1998)
Acta Mathematica Universitatis Comenianae. New Series
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Qun Lin, Tang Liu, Shu Hua Zhang (2009)
Applications of Mathematics
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In this paper we are concerned with finite element approximations to the evaluation of American options. First, following W. Allegretto etc., SIAM J. Numer. Anal. (2001), 834–857, we introduce a novel practical approach to the discussed problem, which involves the exact reformulation of the original problem and the implementation of the numerical solution over a very small region so that this algorithm is very rapid and highly accurate. Secondly by means of a superapproximation and...