Abstract
The pollution effect is a well-known and well-investigated phenomenon of the finite element method for wave problems in general and for acoustic problems in particular. It is understood as the problem that a local mesh refinement cannot compensate the numerical error which is generated and accumulated in other regions of the model. This is the case for the phase error of the finite element method which leads to dispersion resulting in very large numerical errors for domains with many waves in them and is of particular importance for low order elements. Former investigations have shown that a pollution effect resulting from dispersion is unlikely for the boundary element method. However, numerical damping in the boundary element method can account for a pollution effect. A further investigation of numerical damping reveals that it has similar consequences as the phase error of the finite element method. One of these consequences is that the number of waves within the domain may be controlling the discretiz...
Highlights
It is common practice to use a certain fixed number of boundary elements per wavelength in engineering simulations
This paper describes numerical damping observations of both, findings in literature[39] and the author’s own simulations.[18]
Being very similar meshes, a discretization error determined in the L2 norm will be much higher if the wave travels through the coarse grid region first
Summary
Dedicated to Professor Frank Ihlenburg on the occasion of his 60th birthday. The pollution effect is a well-known and well-investigated phenomenon of the finite element method for wave problems in general and for acoustic problems in particular. It is understood as the problem that a local mesh refinement cannot compensate the numerical error which is generated and accumulated in other regions of the model This is the case for the phase error of the finite element method which leads to dispersion resulting in very large numerical errors for domains with many waves in them and is of particular importance for low order elements. A further investigation of numerical damping reveals that it has similar consequences as the phase error of the finite element method One of these consequences is that the number of waves within the domain may be controlling the discretization error in addition to the size and the order of the boundary elements.
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