Multi‐Goal‐Oriented Anisotropic Error Control and Mesh Adaptivity for Time‐Dependent Convection‐Dominated Problems

ABSTRACT In this work, we present an anisotropic multi‐goal error control based on the dual weighted residual (DWR) method for time‐dependent convection–diffusion–reaction (CDR) equations. Motivated by former work, we combine multiple goals to single error functionals with weights chosen as algorithmic parameters. Using anisotropic interpolation and restriction operators, we obtain elementwise error indicators in space and time, where the spatial indicators are additionally separated with respect to the single directions. The directional error indicators quantify anisotropy of the solution with respect to the goals, and produce adaptive, anisotropic meshes that efficiently capture layers. To prevent spurious oscillations the streamline upwind Petrov–Galerkin (SUPG) method is applied to stabilize the underlying system in the case of high Péclet numbers. Numerical examples show efficiency and robustness of the proposed approach for a range of goal quantities using established benchmarks for convection‐dominated transport.