Adaptive Finite element methods

The goal of adaptive finite element methods is to automatically build a meshes sequence that fit the numerical solution. It means fine meshes in the regions where the solution changes rapidly and coarse in the other regions. The refinement/coarsening criterium is based on a posteriori error estimates, the true error being bounded above and below by a computable quantity, the so-called error estimator. Recently, adaptive finite elements and a posteriori error estimates have been developed for highly stretched meshes. The goal is to refine the mesh only in appropriates directions and therefore to reduce the number of mesh vertices.


Recent Publications

D. S. Guignard; F. Nobile; M. Picasso : A posteriori error estimation for the steady Navier-Stokes equations in random domains; Computer Methods in Applied Mechanics and Engineering. 2017. DOI : 10.1016/j.cma.2016.10.008.
D. S. Guignard; F. Nobile; M. Picasso : MATHICSE Technical Report : A posteriori error estimation for the steady Navier-Stokes equations in random domains. 2016-04-18.
D. S. Guignard / F. Nobile; M. Picasso (Dir.) : A posteriori error estimation for partial differential equations with random input data. Lausanne, EPFL, 2016. DOI : 10.5075/epfl-thesis-7260.
D. S. Guignard; F. Nobile; M. Picasso : A posteriori error estimations for elliptic partial differential equations with small uncertainties; Numerical Methods for Partial Differential Equations. 2016. DOI : 10.1002/num.21991.
D. S. Guignard; F. Nobile; M. Picasso : MATHICSE Technical Report : A posteriori error estimations for elliptic partial differential equations with small uncertainties. 2014-07-21.
S. Boyaval; M. Picasso : A posteriori analysis of the Chorin-Temam scheme for Stokes equations; Comptes Rendus Mathematique. 2013. DOI : 10.1016/j.crma.2013.10.026.
Y. Bourgault; M. Picasso; F. Alauzet; A. Loseille : On the use of anisotropic a posteriori error estimators for the adaptative solution of 3D inviscid compressible flows; International Journal For Numerical Methods In Fluids. 2009. DOI : 10.1002/fld.1797.