# Non Overlapping Domain Decomposition for Singularly Perturbed Elliptic Boundary Value Problems

Abstract : We analyze the Funaro-Quarteroni alternative procedure for the solution of singular perturbation problems. We show that for an appropriate choice of the domain decomposition, one obtains a fast convergent iterative scheme with {\it no relaxation} that resolves the boundary layers. The convergence is superlinear with respect to the singular perturbation parameter $\epsilon$ in the following sense: the amplification factor is $o(\epsilon)$. We give sharp estimates of the interface position and convergent rates for an homogeneous domain decomposition in one dimensional space as well as in two dimensional space problems on a disk. We extend our results to heterogeneous domain decomposition arising in a simplified model of an electromagnetic problem. We report on implementation results with finite difference approximations and finite element codes ({\it Modulef})
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https://hal.inria.fr/inria-00073552
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Submitted on : Wednesday, May 24, 2006 - 1:10:47 PM
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### Identifiers

• HAL Id : inria-00073552, version 1

### Citation

Marc Garbey, Laurence Viry, Olivier Coulaud. Non Overlapping Domain Decomposition for Singularly Perturbed Elliptic Boundary Value Problems. [Research Report] RR-3137, INRIA. 1997, pp.45. ⟨inria-00073552⟩

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