Spurious modes in finite-element discretizations of the wave equation may not be all that bad Original Research Article

If higher-order finite elements are used to discretize the wave equation, spurious modes may occur. These modes are classified as unphysical and supposedly make elements of high order useless for accurate computations. This is in conflict with numerical experiments which appear to provide good results. Here Fourier analysis is used to investigate the behaviour of the numerical error for a number of higher-order one-dimensional finite elements. It is shown that the spurious modes have a contribution to the numerical error that behaves in a reasonable manner, and that higher-order elements can be more accurate than lower-order elements. Lumped elements with Gauss–Lobatto nodes appear to be the best choice.