Adaptivity with dynamic meshes for space-time finite element discretizations of parabolic equations

In this paper, we develop an error estimator and an adaptive algorithm for efficient solution of parabolic partial differential equations. The error estimator assesses the discretization error with respect to a given quantity of physical interest and separates the influence of the time and space discretizations. This allows us to set up an efficient adaptive strategy producing economical (locally) refined meshes for each time step and an adapted time discretization. The space and time discretization errors are equilibrated, leading to an efficient method.