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- W2557179416 abstract "Abstract In this paper, we study the extension of anisotropic metric-based mesh adaptation to the case of very high-order solutions in 3D. This work is based on an extension of the continuous mesh framework and multi-scale mesh adaptation [10] where the optimal metric is derived through a calculus of variation. Based on classical high order a priori error estimates [4] , the point-wise leading term of the local error is a homogeneous polynomial of order k + 1. To derive the leading anisotropic direction and orientations, this polynomial is approximated by a quadratic positive definite form, taken to the power . From a geometric point of view, this problem is equivalent to finding a maximal volume ellipsoid included in the level set one of the absolute value of the polynomial. This optimization problem is strongly non-linear both for the functional and the constraints. We first recast the continuous problem in a discrete setting in the metric-logarithm space. With this approximation, this problem becomes linear and is solved with the simplex algorithm [5] . This optimal quadratic form in the Euclidean space is then found by iteratively solving a sequence of such log-simplex problems. From the field of the local quadratic forms that representing the high-order error, a calculus of variation is used to globally control the error in L p norm. A closed form of the optimal metric is then found. Anisotropic meshes are then generated with this metric based on the unit mesh concept [8] . For the numerical experiments, we consider several analytical functions in 3D. Convergence rate and optimality of the meshes are then discussed for interpolation of orders 1 to 5." @default.
- W2557179416 created "2016-11-30" @default.
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- W2557179416 date "2016-01-01" @default.
- W2557179416 modified "2023-10-14" @default.
- W2557179416 title "Very High Order Anisotropic Metric-Based Mesh Adaptation in 3D" @default.
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- W2557179416 doi "https://doi.org/10.1016/j.proeng.2016.11.071" @default.
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