A POD goal-oriented error measure for mesh optimisation

A novel approach for designing an error measure to guide an adaptive meshing algorithm using a POD adjoint or goal-based method, is presented here. In this work the multi-field error measure was applied to each field type at each time level between two points in time where mesh adaptivity is applied. The aim is to obtain a new mesh that can resolve all the fields at all time levels, to an optimal (with respect to the functional) level of accuracy. These goal based methods solve both forward and adjoint equations to form the overall error norms or metric tensors. Once metric tensors are obtained (the focus of this work) the tetrahedral elements are then optimised so that they have unit element lengths and good quality aspect ratios when measured with respect to the metric tensors. Forward and adjoint evolutionary equations are solved to obtain forward and adjoint solutions which together with their