On the stabilized finite element method for steady convection-dominated problems with anisotropic mesh adaptation

In this work, we combine the use of the Streamline Upwind Petrov–Galerkin (SUPG) method with anisotropic mesh adaptation to obtain accurate solutions for steady convection-dominated problems. The anisotropic mesh adaptation framework is introduced in the context of a local mesh generation method based on a mesh topology modification and a minimal volume principle. A new route to get a metric field directly at the node of the mesh is highlighted using the length distribution tensor and an edge based error analysis. An a posteriori error estimation is applied to the stabilized finite element solution detecting automatically all sharp gradients, inner and boundary layers. The numerical examples show that the use of the anisotropic mesh adaptation algorithm allows the recovery of the global convergence order of the numerical schemes while producing accurate and oscillation free numerical solutions.