A general class of Taylor-Galerkin finite element implicit-explicit schemes

This paper proposes a generalised form of the ‘Taylor-Galerkin method’ for convective transport problems. A wide range of existing explicit and implicit methods can be included in this formulation, being always second order accurate in space and time. Furthermore, consistency conditions for higher order schemes can be established, relating, together with stability conditions, the parameters used in the method. The generalization presented allows the election of optimal schemes for stationary or transient processes, taking into account the stability, solvability and phase and amplitude errors. This work includes the linear analysis of a scalar transport equation and the extension of the formulation for non-linear systems in conservation form, being future applications multidimensional convective transport problems.