Higher-order finite elements with mass-lumping for the 1D wave equation

This paper is devoted to the construction and analysis of a method, higher order in space and time, for solving the one-dimensional wave equation. This method is based on P₃ Lagrange finite elements with mass-lumping which avoids the inversion of a mass matrix at each time-step. The mass-lumping implies to make the abscissae of the interior points coincide with these of the Gauss-Lobatto quadrature rule. A Fourier analysis of the method for a regular mesh points out a superconvergence result. The gain of accuracy is illustrated by numerical experiments.