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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
34/2010

Nonconforming least-squares method for elliptic partial differential equations with smooth interfaces

Kishore Kumar Naraparaju and G. Naga Raju

Abstract

In this paper a numerical method based on least-squares approximation is proposed for elliptic interface problems in two dimensions, where the interface is smooth. The underlying method is spectral element method. In the least-squares formulation a functional is minimized as defined in (4.1). The jump in the solution and its normal derivative across the interface are enforced (in an appropriate Sobolev norm) in the functional. The solution is obtained by solving the normal equations using preconditioned conjugate gradient method. Essentially the method is nonconforming, so a block diagonal matrix is constructed as a preconditioner based on the stability estimate where each diagonal block is decoupled. A conforming solution is obtained by making a set of corrections to the nonconforming solution as in [24] and an error estimate in $H^{1}$-norm is given which shows the exponential convergence of the proposed method.

Received:
Jul 20, 2010
Published:
Jul 21, 2010
MSC Codes:
65M70, 65N35, 65Y05
Keywords:
Interface, Spectral element, preconditioner

Related publications

inJournal
2012 Repository Open Access
Kishore Kumar Naraparaju and G. Naga Raju

Nonconforming least-squares method for elliptic partial differential equations with smooth interfaces

In: Journal of scientific computing, 53 (2012) 2, pp. 295-319