Adaptive Lagrange-Galerkin methods for unsteady convection-diffusion problems

In this paper we derive an a posteriori error bound for the Lagrange-Galerk in discretisation of an unsteady (linear) convection-diffusion problem, ass uming only that the underlying space-time mesh is nondegenerate. The proof of this error bound is based on strong stability estimates of an associated dual problem, together with the Galerkin orthogonality of the finite eleme nt method. Based on this a posteriori bound, we design and implement the co rresponding adaptive algorithm to ensure global control of the error with r espect to a user-defined tolerance.