Author(s)

F. Ihlenburg, I. Babuska & S. Sauted

Abstract

Reliability of finite element methods for the numerical computation of waves F. Ihlenburg*, I. Babuska*, S. Sauted "Institute for Physical Science and Technology, University of Maryland at College Park, College Park MD 20740, USA ^Universitdt Kiel, Institutfur Informatik und Praktische Mathematik, D-24118 Kiel, Germany 1 Introduction The numerical computation of stationary waves in exteriour and scatter- ing problems is based on indefinite variational forms connected with the Helmholtz equation Aw + k*u = 0 where k is a real parameter (scalar wavenumber). Unlike the case of linear elasticity, stable dependence of both analytical (if existing) and numerical solutions on the data is not straightforward. Stability estimates of the form \u\t < Cij\f\j do hold for various norms i,j but the constants dj depend in general on the parameter k. Hence also the quality of the discrete solution depends on fc, as well as on the parameters of the numerica

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