Abstract
We present an algorithm that reformulates existing methods to construct higher-order mimetic differential operators. Constrained linear optimization is the key idea of this resulting algorithm. The authors exemplified this algorithm by constructing an eight-order-accurate one-dimensional mimetic divergence operator. The algorithm computes the weights that impose the mimetic condition on the constructed operator. However, for higher orders, the computation of valid weights can only be achieved through this new algorithm. Specifically, we provide insights on the computational implementation of the proposed algorithm, and some results of its application in different test cases. Results show that for all of the proposed test cases, the proposed algorithm effectively solves the problem of computing valid weights, thus constructing higher-order mimetic operators.
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Sanchez, E., Paolini, C., Blomgren, P., Castillo, J. (2015). Algorithms for Higher-Order Mimetic Operators. In: Kirby, R., Berzins, M., Hesthaven, J. (eds) Spectral and High Order Methods for Partial Differential Equations ICOSAHOM 2014. Lecture Notes in Computational Science and Engineering, vol 106. Springer, Cham. https://doi.org/10.1007/978-3-319-19800-2_39
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DOI: https://doi.org/10.1007/978-3-319-19800-2_39
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-19799-9
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