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dc.contributorRuiz-Gironés, Eloi
dc.contributorSarrate Ramos, Josep
dc.contributor.authorPérez Álvarez, Antonio
dc.contributor.otherUniversitat Politècnica de Catalunya. Departament de Matemàtica Aplicada III
dc.date.accessioned2015-10-29T10:49:29Z
dc.date.available2015-10-29T10:49:29Z
dc.date.issued2015-10
dc.identifier.urihttp://hdl.handle.net/2117/78471
dc.description.abstractHigher-order methods in finite elements can provide better approximations than linear methods, in some problems. This is because they can offer an exponential convergence rate of the solution. Thus, in some applications, high-order methods can be cheaper than low-order methods. Nonetheless, it is of major importance to provide good implementations in order to reduce the computational cost of solving a problem. To this end, we propose to use the classical continuous Galerkin method with static condensation procedure to reduce the memory footprint and the CPU time. The main idea consists on write the unknowns related to the inner nodes of each element in terms of the unknowns related to the boundary nodes of the elements. Thus, this method effectively suppress all the unknowns that correspond to pure interior elemental nodes. To show these properties, we apply the static condensation technique to the Poisson problem. We will particularize the proposed technique for this problem, and we will compare the obtained solution and the computational cost with a classical implementation of the high-order continuous Galerkin method. In order to formulate the method correctly, all the needed results are introduced. The results show that static condensation is a valid choice since it reduces the computational cost of solving a problem.
dc.language.isoeng
dc.publisherUniversitat Politècnica de Catalunya
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subjectÀrees temàtiques de la UPC::Matemàtiques i estadística::Anàlisi numèrica
dc.subject.lcshNumerical analysis
dc.subject.otherFinite element method
dc.subject.otherHigh-order methods
dc.subject.otherContinuous Galerkin
dc.subject.otherStatic condensation
dc.subject.otherPoisson.
dc.titleNumerical approximation of Poisson problems using high-order continuous Galerkin methods with static condensation
dc.typeMaster thesis
dc.subject.lemacAnàlisi numèrica
dc.subject.amsClassificació AMS::65 Numerical analysis::65Y Computer aspects of numerical algorithms
dc.identifier.slugFME-1208
dc.rights.accessOpen Access
dc.date.updated2015-10-20T05:38:58Z
dc.audience.educationlevelMàster
dc.audience.mediatorUniversitat Politècnica de Catalunya. Facultat de Matemàtiques i Estadística
dc.audience.degreeMÀSTER UNIVERSITARI EN MATEMÀTICA AVANÇADA I ENGINYERIA MATEMÀTICA (Pla 2010)


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