Output Error Control Using r-Adaptation

Abstract

We present an output-based adaptive error control strategy based on unsteady radaptation, i.e. mesh motion, for the discontinuous Galerkin finite element method. The method uses a discrete unsteady adjoint to compute an error estimate in a scalar output of interest. Localized to space-time elements, this estimate yields an error indicator that identifies regions in space and time where refinement is required to reduce the output error. Rather than employing standard h or p refinement techniques, we adapt the mesh by moving its nodes. This allows elements to grow or shrink without increasing the degrees of freedom. The mesh motion is performed using analytical contraction/expansion functions and node-interpolated motion driven by a spring analogy in an arbitrary Lagrangian-Eulerian framework, and we demonstrate the ability of such motion to reduce output error in scalar advection-diffusion problems.