Numerical dispersion
In the numerical solution of partial differential equations, a discretization error of 3rd order in space is called numerical dispersion . This is used to describe the discretization error not only quantitatively but qualitatively. This approach is particularly useful when dispersive effects play a major role in the physical solution and are superimposed by numerical dispersion.
For example, a numerical solution of the wave equation with finite differences of the 2nd order at higher wave numbers or frequencies deviates more from the analytical solution than would be expected from purely quantitative convergence considerations. The density of the discretization per wavelength must increase with the wave number or frequency, in order to prevent the physical dispersion from being dominated by the numerical dispersion.
Analog plays in the construction of numerical methods for hyperbolic conservation laws , the numerical diffusion an important role as error term of the second order.
literature
- F. Ihlenburg: Finite Element Analysis of Acoustic Scattering . New York: Springer, 1998