Efficiency of Old and New Triangular Finite Elements for Wavefield Modelling in Time

Summary Finite elements with mass lumping allow for explicit time stepping when modelling wave propagation and can be more efficient than finite differences in complex geological settings. In 2D on quadrilaterals, spectral elements are the obvious choice. Triangles are more flexible for meshing, but the construction of polynomial elements is less straightforward. So far, elements up to degree 9 have been found. Some years ago, an accuracy criterion that is sharper and less restrictive than the customary one led to new tetrahedral elements that are considerably more efficient than those previously known. Applying the same criterion to triangular elements provides infinitely many new elements of degree 5, with the same number of nodes as the old one, and two elements of degree 6 with less nodes than the known ones. Their efficiency, measured in terms of the compute time needed to obtain a solution with a given accuracy, is determined for a homogeneous problem and compared to that of the old elements of degree 1 to 8. For moderate accuracy, elements of degree 3 are the most efficient. For high accuracy, one of the new degree-6 elements performs best.