SIAM Journal on Numerical Analysis
Least-Squares Finite Element Approximations to Solutions of Interface Problems
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
Analysis of a Discontinuous Least Squares Spectral Element Method
Journal of Scientific Computing
SIAM Journal on Numerical Analysis
SIAM Journal on Numerical Analysis
The Immersed Interface Method: Numerical Solutions of PDEs Involving Interfaces and Irregular Domains (Frontiers in Applied Mathematics)
Preconditioners for spectral element methods for elliptic and parabolic problems
Journal of Computational and Applied Mathematics
SIAM Journal on Numerical Analysis
hp-Adaptive least squares spectral element method for hyperbolic partial differential equations
Journal of Computational and Applied Mathematics
Optimal a priori estimates for higher order finite elements for elliptic interface problems
Applied Numerical Mathematics
Least-squares hp/spectral element method for elliptic problems
Applied Numerical Mathematics
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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.