Domain decomposition methods have been developed quite systematically for conforming lower order finite element approximations of elliptic problems. These algorithms are preconditioned conjugate gradient methods based on solvers on subregions and certain low dimensional global models. Relatively less attention has been paid to the large linear algebraic systems of equations that arise in discretizations based on spectral elements, the p-version finite elements, and the mortar methods. An overview is given of some of our work on domain decomposition methods for spectral elements, carried out jointly with Luca Pavarino, and on mortar elements, jointly with Yvon Maday. [References: 10]
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