Optimal simplex finite-element approximations of arbitrary order in curved domains circumventing the isoparametric technique
 
 
Description:  One of the reasons for the undeniable success of the finite-element method in the applied sicences is its great versatility to deal with different types of geometries. This is particularly true of problems posed in curved domains of arbitrary shape. In this case method's isoparametric version for meshes consisting of curved triangles or tetrahedra has been mostly employed to recover the optimal approximation properties known to hold for standard straight elements in the case of polygonal or polyhedral domains. However, besides obvious geometric inconveniences, the isoparametric technique helplessly requires the manipulation of rational functions and consequent compulsory use of numerical integration. In this talk a simple alternative is presented that bypasses all the above drawbacks, without eroding qualitative approximation properties. More specifically, the underlying technique is as universal as can be to accurately handle Dirichlet boundary conditions of different types without curved elements. Moreover its implementation is simple, in particular because it is based only on polynomial algebra.
Date:  2017-02-10
Start Time:   14:30
Speaker:  Vitoriano Ruas (Univ. Pierre et Marie Curie, Paris, and Catholic Univ., Rio de Janeiro)
Institution:  Université Pierre et Marie Curie, Paris 6 and Catholic University of Rio de Janeiro
Place:  Room 2.4
Research Groups: -Numerical Analysis and Optimization
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