# Nonconforming Least-Squares Method for Elliptic Partial Differential Equations with Smooth Interfaces

 dc.contributor.author Naraparaju, Kishore Kumar dc.contributor.author Nagaraju, G. dc.date.accessioned 2014-03-16T13:15:51Z dc.date.available 2014-03-16T13:15:51Z dc.date.issued 2012-11 dc.identifier.citation Naraparaju, Kishore Kumar and Naga Raju, G., “Nonconforming least-squares method for elliptic partial differential equations with smooth interfaces”, Journal of Scientific Computing, DOI:10.1007/s10915-011-9572-5, vol. 53, no. 2, pp. 295-319, Nov. 2012. en_US dc.identifier.issn 0885-7474 dc.identifier.issn 1573-7691 dc.identifier.uri http://dx.doi.org/10.1007/s10915-011-9572-5 dc.identifier.uri https://repository.iitgn.ac.in/handle/123456789/794 dc.description.abstract In this paper a least-squares based method is proposed for elliptic interface problems in two dimensions, where the interface is smooth. The underlying method is spectral element method. The least-squares formulation is based on the minimization of a functional 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 Schwab (p and h–p Finite Element Methods, Clarendon Press, Oxford, 1998) and an error estimate in H 1-norm is given which shows the exponential convergence of the proposed method. en_US dc.description.statementofresponsibility by Kishore Kumar Naraparaju and G. Naga Raju dc.format.extent Vol. 53, No. 2, pp. 295-319 dc.language.iso en en_US dc.publisher Springer Link en_US dc.subject Exponential accuracy en_US dc.subject Interface en_US dc.subject Least-squares en_US dc.subject Nonconforming en_US dc.subject Preconditioner en_US dc.subject Spectral element en_US dc.title Nonconforming Least-Squares Method for Elliptic Partial Differential Equations with Smooth Interfaces en_US dc.type Article en_US dc.relation.journal Journal of Scientific Computing
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