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

Show simple item record Naraparaju, Kishore Kumar Nagaraju, G. 2014-03-16T13:15:51Z 2014-03-16T13:15:51Z 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.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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