Effect of Element Distortion on the Numerical Dispersion of Spectral Element Methods (Communications in Computational Physics, 2011)
Spectral element methods are well established in the field of wave propagation,in particular because they inherit the flexibility of finite element methods andhave low numerical dispersion error. The latter is experimentally acknowledged, buthas been theoretically shown only in limited cases, such as Cartesian meshes. It iswell known that a finite element mesh can contain distorted elements that generatenumerical errors for very large distortions. In the present work, we study the effectof element distortion on the numerical dispersion error and determine the distortionrange in which an accurate solution is obtained for a given error tolerance. We also discussa double-grid calculation of the spectral element matrices that preserves accuracyin deformed geometries.