论文信息 - A local projection stabilized method for fictitious domains

A local projection stabilized method for fictitious domains

In this work a local projection stabilization method is proposed for solving a fictitious domain problem. The method adds a suitable fluctuation term to the formulation, thus yielding the natural space for the Lagrange multiplier stable. Stability and convergence are proved and these results are illustrated with a numerical experiment.

Gabriel R. Barrenechea | Franz Chouly

[1] Peter Hansbo,et al. Fictitious domain finite element methods using cut elements: I. A stabilized Lagrange multiplier method , 2010 .

[2] Erik Burman,et al. Pressure projection stabilizations for Galerkin approximations of Stokes' and Darcy's problem , 2008 .

[3] Jean-François Remacle,et al. Imposing Dirichlet boundary conditions in the eXtended Finite Element Method , 2011 .

[4] P. Hansbo,et al. Fictitious domain finite element methods using cut elements , 2012 .

[5] Jaroslav Haslinger,et al. A New Fictitious Domain Approach Inspired by the Extended Finite Element Method , 2009, SIAM J. Numer. Anal..

[6] Michel Fortin,et al. A minimal stabilisation procedure for mixed finite element methods , 2000, Numerische Mathematik.

[7] R. Glowinski,et al. A fictitious domain method for Dirichlet problem and applications , 1994 .

[8] R. Glowinski,et al. Error analysis of a fictitious domain method applied to a Dirichlet problem , 1995 .

[9] J. Guermond,et al. Theory and practice of finite elements , 2004 .