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The accurate and efficient treatment of wave propogation phenomena is still a challenging problem. A prototypical equation is the Helmholtz equation at high wavenumbers. For this equation, Babuˇska & Sauter showed in 2000 in their seminal SIAM Review paper that standard discretizations must fail in the sense that the ratio of true error and best approximation error has to grow with the frequency. This has spurred the development of alternative, non-standard discretization techniques. This workshop focused on evaluating and comparing these different approaches also with a view to their applicability to more general wave propagation problems.
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Jens Markus Melenk, Peter Monk, Christian Wieners, Mini-Workshop: Efficient and Robust Approximation of the Helmholtz Equation. Oberwolfach Rep. 9 (2012), no. 4, pp. 3305–3338DOI 10.4171/OWR/2012/55