000013096 001__ 13096
000013096 005__ 20161114160327.0
000013096 04107 $$aeng
000013096 046__ $$k2009-06-22
000013096 100__ $$aHarari, I.
000013096 24500 $$aStabilized finite element methods for elastic waves

000013096 24630 $$n2.$$pComputational Methods in Structural Dynamics and Earhquake Engineering
000013096 260__ $$bNational Technical University of Athens, 2009
000013096 506__ $$arestricted
000013096 520__ $$2eng$$aStandard, 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.

000013096 540__ $$aText je chráněný podle autorského zákona č. 121/2000 Sb.
000013096 653__ $$aElastic Waves, Finite Elements, Stabilized Methods, Dispersion, Polarization. Abstract. 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.

000013096 7112_ $$aCOMPDYN 2009 - 2nd International Thematic Conference$$cIsland of Rhodes (GR)$$d2009-06-22 / 2009-06-24$$gCOMPDYN2009
000013096 720__ $$aHarari, I.$$iGanel, R.$$iGrosu, E.
000013096 8560_ $$ffischerc@itam.cas.cz
000013096 8564_ $$s464289$$uhttps://invenio.itam.cas.cz/record/13096/files/CD127.pdf$$yOriginal version of the author's contribution as presented on CD, section: Semi-plenary lectures.
000013096 962__ $$r13074
000013096 980__ $$aPAPER