Optimization-based anisotropic mesh-polynomial adaptation for high-order methods

Abstract eng:
We present a general framework for anisotropic hp-adaptation of high-order discontinuous Galerkin finite element discretizations for compressible flow simulation. Using the sensitivities of an adjoint-based error estimate our method seeks optimal element mesh size h and polynomial degree p distributions. This approach results in an optimal hp-mesh tailored to yield the most accurate prediction of a quantity of interest, such as aerodynamic coefficients, at a given computational cost (number of degrees of freedom). The proposed approach features a reduced dependence on the initial mesh compared to established adjoint-based adaptive methods. It provides a unifying framework where adaptation choices such as isotropic/anisotropic, h-/p-refinement/coarsening do not only rely on local arbitrary measures of the solution’s anisotropy and smoothness, but rather where a globally optimal distribution of degrees of freedom is sought to minimize the error in the chosen quantity of interest.

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