Thursday, October 27, 9:30 am in room MTH 3206, University of Maryland,
College Park
Error estimation of Galerkin FEM for the numerical computation of waves
Dr. Frank Ihlenburg
Technical University of Wismar, Germany
soihfr@hsw-serv.hs-wismar.de
We consider the numerical computation of stationary waves in exteriour and
scattering problems by finite element methods. The quality of the discrete
solution depends on the parameter of the wave equation (frequency) and the
parameters of the numerical model (stepwidth h, degree of approximation
p). For practical application it is essential to have reliable "rules of
the thumb" for the choice of the numerical parameters as a function of
physical parameters. It was found from benchmark computations that a linear
rule is applicable only in the low frequency range. The problem is analyzed
on a one-dimensional model problem. We give error estimates in integral
norms for the h-version of the Galerkin FEM with general degree of
approximation. We show that the discretization error is numerically
polluted by a term depending on the frequency. In the low frequency range,
this term is negligible and a linear rule applies. By including the
pollution term into the estimate, we also generalize previously known
estimates that hold on highly refined mesh. The results are discussed in
the context of physical dispersion analysis. Numerical results of one and
two-dimensional computations will be presented and conclusions for
application will be given.
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