Least-Squares Finite Element Approximations to Solutions of Interface Problems
Authors:
- Yanzhao CaoYCYanzhao Cao
- Max D. GunzburgerMGMax D. Gunzburger
- 1 February 1998
- journal article
- Published by Society for Industrial & Applied Mathematics (SIAM) in SIAM Journal on Numerical Analysis
- Vol. 35 (1) , 393-405
Abstract
A least-squares finite element method for second-order elliptic boundary value problems having interfaces due to discontinuous media properties is proposed and analyzed. Both Dirichlet and Neumann boundary data are treated. The boundary value problems are recast into a first-order formulation to which a suitable least-squares principle is applied. Among the advantages of the method are that nonconforming, with respect to the interface, approximating subspaces may be used. Moreover, the grids used on each side of an interface need not coincide along the interface. Error estimates are derived that improve on other treatments of interface problems and a numerical example is provided to illustrate the method and the analyses.Keywords
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