The Dual Mixed Finite Element Method for the Heat Diffusion Equation in a Polygonal Domain, I

Farhloul, Mohamed; Korikache, Réda; Paquet, Luc

doi:10.1007/978-3-7643-7794-6_16

Cited by 2 publications

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“…belonging to the stochastic Sobolev space S −1,k,H 2 (D) (see (4) for its definition)). Our contribution here consists in introducing a stochastic version of the dual mixed formulation (see [11] for the nonstochastic case) for the stochastic heat diffusion equation (1) in a polygonal domain with a reentrant corner and proving a-priori optimal error estimates for the semi-discretized problem. Thus additionally to the unknown random temperature u, in the mixed formulation, the random heat flux p = K ♦ − → ∇u is considered as an additional unknown.…”

Section: Introductionmentioning

confidence: 99%

Mixed finite element method for the heat diffusion equation in a random medium

Paquet

Korikache

2010

Stochastics

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We introduce the dual mixed method for the heat evolution equation in a polygonal domain D with a random diffusion coefficient K and heat flux − → p = K♦ − → ∇u, ♦ denoting the Wick product. We prove a-priori error estimates for the semi-discrete solution ( − → p h , u h ) of lowest order of the dual mixed method having K-dimensional polynomial chaos expansion of degree N . Due to the reentrant corner of the polygonal domain D, appropriate refinement rules must be imposed on the family of triangulations in order to recapture convergence of order one in space.

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Section: Introductionmentioning

confidence: 99%