Palestras e Seminários

27/03/2019

10:00

auditório Luiz Antonio Favaro (sala 4-111)

Palestrante: Vitoriano Ruas

Responsável: Roberto Ausas (Este endereço de email está sendo protegido de spambots. Você precisa do JavaScript ativado para vê-lo.)

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One of the reasons for the undeniable success of the finite element method is its
versatility to deal with different types of geometries. This is particularly true of curved
domains on whose boundary Dirichlet conditions are prescribed. In the case of second
order boundary value problems in standard Galerkin formulation method's isoparametric
version for meshes consisting of curved triangles or tetrahedrons is a very popular
solution. It has been mostly employed to recover the optimal approximation properties
known to hold for straight-edged Lagrange elements in the case of polytopic domains.
However, besides other inconveniences, the isoparametric technique involves the
manipulation of rational functions and thus the use of numerical integration to compute
element matrices is required. In such a context the choice of right quadrature rules can
turn to a sort of headache, in case complex non linear problems are at hand. Moreover
isoparametric versions for other types of formulations and methods are still incipient.
In this talk a simple alternative to bypass these drawbacks is presented. More precisely
it is a technique based only on polynomial algebra, that can do without curved elements,
though not eroding qualitative approximation properties. Examples with classical
Lagrange finite elements are given for both two- and three-dimensional problems.
Applications with Hermite finite elements illustrate new method's great generality.

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