Finite element solution of a nonlinear diffusion problem with a moving boundary

Čermák, Libor; Zlámal, Miloš

doi:10.1007/bfb0076083

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Cited by 3 publications

(2 citation statements)

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“…In order to simplify problem P c , we introduce a new problem P u using a non-linear transformation. We consider the mapping F : (c 1 , c 2 , c 5 …”

Section: The Mathematical Modelmentioning

confidence: 99%

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Chemical Attack in Free Boundary Domains

Clain¹

1999

Journal of Applied Analysis

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“…In order to simplify problem P c , we introduce a new problem P u using a non-linear transformation. We consider the mapping F : (c 1 , c 2 , c 5 …”

Section: The Mathematical Modelmentioning

confidence: 99%

“…Furthermore, they assume the boundary to be a given function [5] or they take a simplified boundary condition [2].…”

Section: Introductionmentioning

confidence: 99%

Chemical Attack in Free Boundary Domains

Clain¹

1999

Journal of Applied Analysis

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An integrated material removal model for silicon dioxide layers in chemical mechanical polishing processes

Seok

2009

Wear

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Finite-Element Approximation of Elliptic Equations with a Neumann or Robin Condition on a Curved Boundary

Barrett

Elliott

1988

IMA J Numer Anal

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This paper considers a finite-element approximation of a second-order selfadjoint elliptic equation in a region flcR" (with n = 2 or 3) having a curved boundary dQ on which a Neumann or Robin condition is prescribed. If the finite-element space denned over D h , a union of elements, has approximation power h k in the L 2 norm, and if the region of integration is approximated by Q* with dist (Q, £?*) =£ Ch k , then it is shown that one retains optimal rates of convergence for the error in the H 1 and L 2 norms, whether Q* is fitted (£^ = D h) or unfitted (Q* c £>*), provided that the numerical integration scheme has sufficient accuracy.

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Finite element solution of a nonlinear diffusion problem with a moving boundary

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Cited by 3 publications

References 4 publications

Chemical Attack in Free Boundary Domains

Chemical Attack in Free Boundary Domains

An integrated material removal model for silicon dioxide layers in chemical mechanical polishing processes

Finite-Element Approximation of Elliptic Equations with a Neumann or Robin Condition on a Curved Boundary

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