Skip to Main content Skip to Navigation

Multiscale finite element methods for advection-diffusion problems

Abstract : This work essentially deals with the development and the study of multiscale finite element methods for multiscale advection-diffusion problems in the advection-dominated regime. Two types of approaches are investigated: Take into account the advection in the construction of the approximation space, or apply a stabilization method. We begin with advection-dominated advection-diffusion problems in heterogeneous media. We carry on with advection-dominated advection-diffusion problems posed in perforated domains.Here, we focus on the Crouzeix-Raviart type boundary condition for the construction of the multiscale finite elements. We consider two different situations depending on the condition prescribed on the boundary of the perforations: the homogeneous Dirichlet condition or the homogeneous Neumann condition. This study relies on a coercivity assumption.Lastly, we consider a general framework where the advection-diffusion operator is not coercive, possibly in the advection-dominated regime. We propose a Finite Element approach based on the use of an invariant measure associated to the adjoint operator. This approach is unconditionally well-posed in the mesh size. We compare it numerically to a standard stabilization method
Document type :
Complete list of metadata

Cited literature [91 references]  Display  Hide  Download
Contributor : ABES STAR :  Contact
Submitted on : Wednesday, May 24, 2017 - 11:05:06 AM
Last modification on : Wednesday, May 27, 2020 - 10:34:02 AM
Long-term archiving on: : Monday, August 28, 2017 - 4:35:45 PM


Version validated by the jury (STAR)


  • HAL Id : tel-01527285, version 1



François Madiot. Multiscale finite element methods for advection-diffusion problems. General Mathematics [math.GM]. Université Paris-Est, 2016. English. ⟨NNT : 2016PESC1052⟩. ⟨tel-01527285⟩



Record views


Files downloads