Stabilized finite element methods for elastic waves

Abstract eng:
Standard, low-order, continuous Galerkin, finite element methods are unable to cope with wave phenomena at short wave lengths because the computational effort required to resolve the waves and control numerical dispersion errors becomes prohibitive. The failure to adequately represent subgrid scales misses not only the fine-scale part of the solution, but often causes severe pollution of the solution on the resolved scale as well. Since computation naturally separates the scales of a problem according to the mesh size, multiscale considerations provide a useful framework for viewing these difficulties and developing methods to counter them. The Galerkin/least-squares (GLS) method arises in multiscale settings, and its mesh-dependent stability parameter is often defined by dispersion considerations. The application of the GLS method to time-harmonic elastic waves must account for polarization errors in addition to dispersion. A promising definition of the stability parameter that improves on previous work by eliminating dispersion errors of both longitudinal and transverse waves leads to considerable deterioration of the polarization. An alternative definition that balances dispersion and polarization errors provides the best performance.

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