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dc.contributor.authorBadia, Santiago
dc.contributor.authorBonilla de Toro, Jesús
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament d'Enginyeria Civil i Ambiental
dc.date.accessioned2017-01-25T19:08:29Z
dc.date.available2019-02-01T01:31:38Z
dc.date.issued2017-01
dc.identifier.citationBadia, S., Bonilla, J. Monotonicity-preserving finite element schemes based on differentiable nonlinear stabilization. "Computer methods in applied mechanics and engineering", Gener 2017, vol. 313, p. 133-158.
dc.identifier.issn0045-7825
dc.identifier.urihttp://hdl.handle.net/2117/100080
dc.description.abstractIn this work, we propose a nonlinear stabilization technique for scalar conservation laws with implicit time stepping. The method relies on an artificial diffusion method, based on a graph-Laplacian operator. It is nonlinear, since it depends on a shock detector. Further, the resulting method is linearity preserving. The same shock detector is used to gradually lump the mass matrix. The resulting method is LED, positivity preserving, and also satisfies a global DMP. Lipschitz continuity has also been proved. However, the resulting scheme is highly nonlinear, leading to very poor nonlinear convergence rates. We propose a smooth version of the scheme, which leads to twice differentiable nonlinear stabilization schemes. It allows one to straightforwardly use Newton’s method and obtain quadratic convergence. In the numerical experiments, steady and transient linear transport, and transient Burgers’ equation have been considered in 2D. Using the Newton method with a smooth version of the scheme we can reduce 10 to 20 times the number of iterations of Anderson acceleration with the original non-smooth scheme. In any case, these properties are only true for the converged solution, but not for iterates. In this sense, we have also proposed the concept of projected nonlinear solvers, where a projection step is performed at the end of every nonlinear iterations onto a FE space of admissible solutions. The space of admissible solutions is the one that satisfies the desired monotonic properties (maximum principle or positivity).
dc.format.extent26 p.
dc.language.isoeng
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica::Mètodes en elements finits
dc.subject.lcshFinite element method
dc.subject.otherFinite elements
dc.subject.otherDiscrete maximum principle
dc.subject.otherMonotonicity
dc.subject.otherNonlinear solvers
dc.subject.otherShock capturing
dc.titleMonotonicity-preserving finite element schemes based on differentiable nonlinear stabilization
dc.typeArticle
dc.subject.lemacElements finits, Mètode dels
dc.contributor.groupUniversitat Politècnica de Catalunya. ANiComp - Anàlisi numèrica i computació científica
dc.identifier.doi10.1016/j.cma.2016.09.035
dc.description.peerreviewedPeer Reviewed
dc.relation.publisherversionhttp://www.sciencedirect.com/science/article/pii/S0045782516306405
dc.rights.accessOpen Access
local.identifier.drac19257227
dc.description.versionPostprint (author's final draft)
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/FP7/611636/EU/NUMERICAL METHODS AND TOOLS FOR KEY EXASCALE COMPUTING CHALLENGES IN ENGINEERING AND APPLIED SCIENCES/NUMEXAS
dc.relation.projectidinfo:eu-repo/grantAgreement/EC/FP7/258443/EU/Computational Methods for Fusion Technology/COMFUS
local.citation.authorBadia, S.; Bonilla, J.
local.citation.publicationNameComputer methods in applied mechanics and engineering
local.citation.volume313
local.citation.startingPage133
local.citation.endingPage158


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