Fictitious domain methods using cut elements: III. A stabilized Nitsche method for Stokes' problem. (22nd April 2014)

• Record Type: Journal Article
• Authors: Burman, Erik; Hansbo, Peter
• Is Part Of: Mathematical modelling and numerical analysis. Volume 48:Part 3(2014)
• Page Start: 859
• Page End: 874
• Publication Date: 2014-04-22
• Subjects: Finite element methods, -- stabilized methods, -- penalty methods, -- Stokes' problem, -- fictitious domain; Numerical analysis -- Periodicals; Mathematical models -- Periodicals; 510
• DOI: 10.1051/m2an/2013123
• Languages: English
• ISSNs: 0764-583X

Abstract

Abstract : We extend our results on fictitious domain methods for Poisson's problem to the case of incompressible elasticity, or Stokes' problem. The mesh is not fitted to the domain boundary. Instead boundary conditions are imposed using a stabilized Nitsche type approach. Control of the non-physical degrees of freedom, i.e., those outside the physical domain, is obtained thanks to a ghost penalty term for both velocities and pressures. Both inf-sup stable and stabilized velocity pressure pairs are considered.