Higher Order Sparse Grid Methods for Elliptic Partial Differential Equations with Variable Coefficients
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We present a method for discretizing and solving general elliptic partial differential equations on sparse grids employing higher order finite elements. On the one hand, our approach is charactarized by its simplicity. The calculation of the occurring functionals is composed of basic pointwise or unidirectional algorithms. On the other hand, numerical experiments prove our method to be robust and accurate. Discontinuous coefficients can be treated as well as curvilinearly bounded domains. When applied to adaptively refined sparse grids, our discretization results to be highly efficient, yielding balanced errors on the computational domain.
AMS Subject Classification65N30 65N50 65N55
Keywordssparse grids hierarchical finite elements higher order finite elements numerical treatment of boundary value problems
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