Goal-oriented mesh adaptivity for multi-dimension SPN equations
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We present a mesh adaptivity strategy that incorporates, via adjoint calculations, the relative importance of computational regions towards a quantity of interest, a technique known as goal-oriented mesh adaptivity. In this approach, the mesh refinement is still dictated by the error in the forward solution, but it is also weighted by the importance of the solution towards a given goal. Quantities of interest may include reaction rates in a sub domain, pointwise flux values, etc. We have implemented goal-oriented mesh adaptivity for the multi-D (2- and 3-D) SPN equations and propose some numerical results demonstrating the superiority of the goal-oriented approach against the standard adaptivity technique.