Probabilistic Solution of the Dirichlet Problem for Biharmonic Functions in Discrete Space
نویسندگان
چکیده
منابع مشابه
Probabilistic Solution of the Dirichlet Problem for Biharmonic Functions in Discrete Space'
Considering difference equations in discrete space instead of differential equations in Euclidean space, we investigate a probabilistic formula for the solution of the Dirichlet problem for biharmonic functions. This formula involves the expectation of a weighted sum of the pay-offs at the successive times at which the Markov chain is in the complement of the domain. To make the infinite sum co...
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We consider the biharmonic Dirichlet problem on a polygonal domain. Regularity estimates in terms of Sobolev norms of fractional order are proved. The analysis is based on new interpolation results which generalizes Kellogg’s method for solving subspace interpolation problems. The Fourier transform and the construction of extension operators to Sobolev spaces on R are used in the proof of the i...
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A multigrid preconditioning scheme for solving the Ciarlet-Raviart mixed method equations for the biharmonic Dirichlet problem is presented. In particular, a Schur complement formulation for these equations which yields non-inherited quadratic forms is considered. The preconditioning scheme is compared with a standard W-cycle multigrid iteration. It is proved that a Variable V-cycle preconditio...
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A Legendre spectral Galerkin method is presented for the solution of the biharmonic Dirichlet problem on a square. The solution and its Laplacian are approximated using the set of basis functions suggested by Shen, which are linear combinations of two Legendre polynomials. A Schur complement approach is used to reduce the resulting linear system to one involving the approximation of the Laplaci...
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ژورنال
عنوان ژورنال: The Annals of Probability
سال: 1984
ISSN: 0091-1798
DOI: 10.1214/aop/1176993292