Anisotropic meshing with time-stepping control for unsteady convection-dominated problems

In this work, we develop a new anisotropic space and time adaptive method for convection dominated problems with inner and boundary layers. A new route to construct a metric field directly at the nodes of the mesh is highlighted using the length distribution tensor and an edge based error analysis. A Streamline Upwind Petrov-Galerkin (SUPG) finite element method is employed to solve the unsteady convection-diffusion equation. The numerical experiments show that the use of both space and time adaptivity generates optimal time stepping, allows the recovery of the global convergence order of the numerical schemes, reduces the computational time and cost and produces accurate and oscillation free numerical solutions.