The translation operator. Applications to nonlinear reconstruction operators on nonuniform grids
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AuthorAmat Plata, Sergio; Ortiz, Pedro; Ruiz Álvarez, Juan; Trillo Moya, Juan Carlos; Yáñez Avendaño, Dionisio Félix
Knowledge AreaMatemática Aplicada
Realizado en/conUniversidad Politécnica de Cartagena; Universidad de Valencia
Bibliographic CitationS. Amat, P. Ortiz, J. Ruiz, J.C. Trillo, D.F. Yáñez, The translation operator. Applications to nonlinear reconstruction operators on nonuniform grids, Mathematics and Computers in Simulation, Volume 203, 2023, Pages 408-424, ISSN 0378-4754, https://doi.org/10.1016/j.matcom.2022.05.031.
In this paper, we define a translation operator in a general form to allow for the application of the weighted harmonic mean in different applications. We outline the main steps to follow to define adapted methods using this tool. We give a practical example by improving the behavior of a nonlinear reconstruction operator defined in nonuniform grids, which was initially meant to work well with strictly convex data. With this improvement, the reconstruction can be now applied to data coming from smooth functions, retaining the expected maximum approximation order even around the inflection point areas, and maintaining convexity properties of the initial data. This adaptation can be carried out for general nonuniform grids, although to get the theoretical results about the approximation order, we require to work with quasi-uniform grids. We check the theoretical results through some numerical experiments.
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