Open AccessHigh order optimal anisotropic mesh adaptation using hierarchical elements
Author(s) -
Richard Bois,
M. Fortin,
A. Fortin,
A. Couët
Publication year - 2012
Publication title -
european journal of computational mechanics
Language(s) - English
Resource type - Journals
eISSN - 2642-2085
pISSN - 2642-2050
DOI - 10.13052/17797179.2012.702431
Subject(s) - finite element method , polygon mesh , degree (music) , interpolation (computer graphics) , mathematics , discretization , degree of a polynomial , metric (unit) , lagrange polynomial , mathematical optimization , metric tensor , computer science , mathematical analysis , polynomial , geometry , physics , frame (networking) , engineering , operations management , acoustics , thermodynamics , geodesic , telecommunications
Anisotropic mesh adaptation has made spectacular progress in the past few years. The introduction of the notion of a metric, directly linked to the interpolation error, has allowed to control the elongation of elements as well as the discretisation error. This approach is however essentially restricted to linear (P(1)) finite element solutions, though there exists some generalisations. A completely general approach leading to optimal meshes and this, for finite element solution of any degree, is still missing. This is precisely the goal of this work where we show how to estimate the error on a finite element solution of degree k using hierarchical basis for Lagrange finite element polynomials. We then show how to use this information to produce optimal anisotropic meshes in a sense that will be precised.