More Continuous Mass-Lumped Triangular Finite Elements

Abstract When solving the wave equation with finite elements, mass lumping allows for explicit time stepping, avoiding cost of a lower-upper decomposition large sparse matrix. Mass on reference element amounts to numerical quadrature. The weights should be positive stable stepping and preserve accuracy. standard triangular polynomial except linear element, do not have these properties. Accuracy can preserved by augmenting them higher-degree polynomials in interior. This leaves search elements weights, which were found up degree 9 various authors. classic accuracy condition, however, is too restrictive. A sharper, less restrictive condition recently led new mass-lumped tetrahedral 4. Compared known ones 3, they nodes are computationally more efficient. same criterion applied here construction elements. For degrees 2 4, turn out identical ones. 5, number as but now there infinitely many solutions. Some considerably larger stability limit stepping. 6, two than 7, one was negative weight, making it useless equation. If Numerical tests homogeneous wave-propagation problem point source confirm expected require compute those obtained criterion.