Analysis of spurious eigenmodes in finite element equations

Abstract

Numerical analysis of difference schemes often reveals the presence of eigenmodes which do not feature in the continuum solution. An examination of the dispersion relation shows how the spurious and physical modes interact. The behaviour of certain wave-profiles was predicted using this analysis and the results confirmed by numerical experiment. 'New address. British Gas Corporation, Engineering Research Station, Harvey Combe, Killingworth P.O. Box 1 LH, Newcastle-upon-Tyne, NE99 ILH.

Taylor–least‐squares finite element for two‐dimensional advection‐dominated unsteady advection–diffusion problems

“…26 One way of measuring the accuracy of a numerical scheme is to compare the modulus and argument of a numerical eigenvalue to those of the continuum eigenvalue. For the amplitude error define iku A t t , = e -.…”

“…Note that because one continuum equation is approximated by two discrete equations, one for the primary unknown and the other for its derivative, there are two eigenvalues, physical and computational, associated with a numerical scheme when the cubic element is used. 26 One way of measuring the accuracy of a numerical scheme is to compare the modulus and argument of a numerical eigenvalue to those of the continuum eigenvalue. For the amplitude error define Polar plots of the amplitude and phase errors are given in Figure 1, and the discrete L2-error (<), measured by (22) with a normalization factor of unity, is given in Table I: where y j is a discrete value of either R or 0, and N is the total number of discrete points.…”