A method of Lagrange--Galerkin of second order in time
Résumé
The Lagrange--Galerkin method is the coupling of a finite element method for space discretisation with the method of characteristics for the discretisation of the material derivative in some parabolic problems. We propose a new scheme of second-order accuracy in time, which in contrast with previous methods does not require a correction term. Numerical examples, including Burgers equation, illustrate the convergence rate and low computational cost of the method.