This work presents an output-based anisotropic mesh optimization algorithm that builds on previous work of Yano. The distinguishing new feature is a simple error sampling approach for determining the convergence rate tensor of the error on a single element in a finite-element discretization. This approach does not require refinement of the element, nor any additional solves or residual evaluations. Instead, all calculations take place on the original mesh, using fine-space adjoint projections that reflect the extra resolution introduced by a sampled refinement option. The sampling is efficient and relatively simple to implement as it does not require mesh manipulation. Results for various cases demonstrate that the mesh optimization adds resolution and creates anisotropy as expected, and that it performs well compared to uniform refinement strategies and heuristic anisotropy detection methods.
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