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dc.contributor.authorDarrigrand V.en_US
dc.contributor.authorPardo D.en_US
dc.contributor.authorChaumont-Frelet T.en_US
dc.contributor.authorGómez-Revuelto I.en_US
dc.contributor.authorGarcia-Castillo E.en_US
dc.date.accessioned2020-10-16T14:22:57Z
dc.date.available2020-10-16T14:22:57Z
dc.date.issued2020-01
dc.identifier.urihttp://hdl.handle.net/20.500.11824/1171
dc.description.abstractIn this work, we introduce a novel hp-adaptive strategy. The main goal is to minimize the complexity and implementational efforts hence increasing the robustness of the algorithm while keeping close to optimal numerical results. We employ a multi-level hierarchical data structure imposing Dirichlet nodes to manage the so-called hanging nodes. The hp-adaptive strategy is based on performing quasi-optimal unre finements. Taking advantage of the hierarchical structure of the basis functions both in terms of the element size h and the polynomial order of approximation p, we mark those with the lowest contributions to the energy of the solution and remove them. This straightforward unrefi nement strategy does not need from a fi ne grid or complex data structures, making the algorithm flexible to many practical situations and existing implementations. On the other side, we also identify some limitations of the proposed strategy, namely: (a) data structures only support isotropic h-re nements (although p-anisotropic re nements are enabled), (b) we assume certain quasi-orthogonality properties of the basis functions in the energy norm, and (c) in this work, we restrict to symmetric and positive defi nite problems. We illustrate these and other advantages and limitations of the proposed hp-adaptive strategy with several one-, two- and three-dimensional Poisson examples.en_US
dc.formatapplication/pdfen_US
dc.language.isoengen_US
dc.publisherFinite Elements in Analysis and Designen_US
dc.rightsinfo:eu-repo/semantics/openAccessen_US
dc.rights.urihttp://creativecommons.org/licenses/by-nc-sa/3.0/es/en_US
dc.subjecthp-Adaptivityen_US
dc.subjectUnre nementsen_US
dc.subjectElliptic problemsen_US
dc.subjectMulti-levelen_US
dc.titleA Painless Automatic hp-Adaptive Strategy for Elliptic Problemsen_US
dc.typeinfo:eu-repo/semantics/articleen_US
dc.typeinfo:eu-repo/semantics/submittedVersionen_US
dc.identifier.doij.finel.2020.103424
dc.relation.publisherversionhttps://www.sciencedirect.com/science/article/abs/pii/S0168874X20301049en_US


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