A Comparison of Triangular Mass-lumped Finite Elements for 2D Wave Propagation

Mass-lumped continuous finite elements provide accurate solutions of the second-order acoustic or elastic wave equation in complex geological settings, in particular in the presence of topography and large impedance contrasts. Elements of higher polynomial degree have better accuracy than those of lower degree but are also more costly. Here, the performance of elements of degree 1 to 6 is compared for a simple acoustic test problem. The element of degree 6 is new. The numerical test confirm the increase of accuracy with the polynomial degree of the basis functions. In terms of computational cost, the element of degree 4 performs best in the specific example. For higher degrees, the cost of having extra nodes and a more restrictive stability constraint on the time step can no longer be compensated by having a smaller number of larger triangular elements. Only at very high accuracy, the new element of degree 6 wins.