Discontinuous Galerkin methods for elliptic problems with discontinuous coefficients are discussed. First the error bound of the methods is analyzed. Then a multilevel additive Schwarz preconditioner for one of the discrete problems is designed and analyzed. Although the preconditioner is not optimal it is very well suited for parallel computations and its rate of convergence is independent of the jumps of coefficients.
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Maksymilian Dryja (2003) studied this question.
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