Adaptive Mesh Refinement Based on a Posteriori Error Estimation

Adaptive Mesh Refinement Based on a Posteriori Error Estimation Martin Juhas Master of Applied Science Graduate Department of Aerospace Engineering University of Toronto 2014 This thesis describes the application of a h-refinement, adjoint-based, a posteriori error estimation strategy with a solution-driven, block-based adaptive mesh refinement (AMR), finite-volume scheme to the solution of advection-diffusion problems in two dimension. Error-based criteria following from the adjoint-weighted computable correction of a functional, error in the computable correction for the functional, using either primal, dual, or both error formulations, and/or the total estimated error in the functional are all used to direct the mesh refinement in the block-based AMR scheme. The test cases considered here for the advection-diffusion equation illustrate the ability of the error-based AMR criteria to improve the accuracy of integrated functionals where physics-based AMR criteria may fail. The performance of the adjoint-based refinement criteria is compared with both gradient-based and uniform mesh refinement strategies.

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