Abstract
Computation naturally separates scales of a problem according to the mesh size. A variety of improved numerical methods are described by multiscale considerations, differing in the treatment of the unresolved, fine scales. The discontinuous enrichment method provides a unique multiscale approach to computation by employing fine scales that contain solutions of the homogeneous partial differential equation in a discontinuous framework. The method thus combines relative ease of implementation with improved numerical performance. These properties are demonstrated for both multiscale wave and transport problems, pointing to the potential of considerable savings in computational resources.
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