Huttunen, T.; Monk, P.; Collino, F.; Kaipio, J. P. The ultra-weak variational formulation for elastic wave problems. (English) Zbl 1093.74028 SIAM J. Sci. Comput. 25, No. 5, 1717-1742 (2004). Summary: The ultra-weak variational formulation has been used to solve time-harmonic acoustic and electromagnetic wave propagation in inhomogeneous media. We develop the ultra-weak variational formulation for elastic wave propagation in two space dimensions. In order to improve the accuracy and stability of the method, we find it necessary to approximate the \(S\)- and \(P\)-wave components of the solution in a balanced way. Some preliminary analysis is provided and numerical evidence is presented of the efficiency of the scheme in comparison to piecewise linear finite elements. Cited in 37 Documents MSC: 74J10 Bulk waves in solid mechanics 74J20 Wave scattering in solid mechanics 74S05 Finite element methods applied to problems in solid mechanics Keywords:scattering; finite element method; Lamé equations PDFBibTeX XMLCite \textit{T. Huttunen} et al., SIAM J. Sci. Comput. 25, No. 5, 1717--1742 (2004; Zbl 1093.74028) Full Text: DOI