A time‐space FCT‐FE formulation for 1D time dependent advection‐diffusion equation

Abstract

AbstractWe present a time‐space flux‐corrected transport (FCT) finite element formulation for solving the linear time‐dependent advection dominated advection‐diffusion equation. Solving advection dominated transport equations with conventional finite element (FE) methods suffers from drawbacks of excessive numerical dispersion which results in non‐physical, non‐monotonic solutions. The FCT algorithm is an effective method which suppresses the non‐monotonic behavior of the solution by applying a limited anti‐diffusion operator to a first order scheme. Applying the FCT algorithm to time‐space FE formulation, such as the time‐discontinuous Galerkin (TDG) method, benefits from the advantages of both the TDG scheme and the FCT algorithm. In another word, the time‐space FCT‐FE formulation achieves arbitrary odd order accuracy in time at the discontinuous time nodes. Large time steps can be applied and the scheme ensures monotonic solution when linear interpolation is used for spatial discretization.