EFFECT OF ELEMENT DISTORTION ON THE NUMERICAL DISPERSION OF SPECTRAL ELEMENT METHODS

Spectral elements are well established in the field of computational seismology, specially because they inherit the flexibility of finite element methods and have low numerical dispersion error. The latter is experimentally acknowledged, but is theoretically known in limited cases, such as Cartesian meshes [2]. It is well known that a finite element mesh can contain distorted elements that generate numerical errors for very large distortion. In the present work we study the effect of element distortion on the numerical dispersion error and determine the distortion range in which an accurate solution is obtained with a given error tolerance. We consider spectral elements for the 2D acoustic wave equation ¨(x,t) = c 2 u(x,t). Let us write its semi-dicretization in space in the form M ¨ u (t) + c 2 Ku = 0, where u p(t) u(xp,t) and M,K are the mass and stiffness matrices, respectively. Plugging into this system a harmonic plane wave u (t) = exp( i! t)w, wp = exp(i · xp), we find

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