Cut finite element methods for coupled bulk–surface problems

作者: Erik Burman , Peter Hansbo , Mats G. Larson , Sara Zahedi

DOI: 10.1007/S00211-015-0744-3

关键词: Finite element methodMathematicsExtended finite element methodCondition numberApplied mathematicsMixed finite element methodSmoothed finite element methodhp-FEMAlgorithmFinite element limit analysisNumerical analysisComputational mathematics

摘要: We develop a cut finite element method for second order elliptic coupled bulk-surface model problem. prove priori estimates the energy and $$L^2$$L2 norms of error. Using stabilization terms we show that resulting algebraic system equations has similar condition number as standard fitted method. Finally, present numerical example illustrating accuracy robustness our approach.

参考文章(17)
L. Ridgway Scott, Susanne C Brenner, The Mathematical Theory of Finite Element Methods ,(2007)
Erik Burman, Susanne Claus, Peter Hansbo, Mats G. Larson, André Massing, CutFEM: Discretizing geometry and partial differential equations International Journal for Numerical Methods in Engineering. ,vol. 104, pp. 472- 501 ,(2015) , 10.1002/NME.4823
M.R. Booty, M. Siegel, A hybrid numerical method for interfacial fluid flow with soluble surfactant Journal of Computational Physics. ,vol. 229, pp. 3864- 3883 ,(2010) , 10.1016/J.JCP.2010.01.032
Maxim A. Olshanskii, Arnold Reusken, Jörg Grande, A Finite Element Method for Elliptic Equations on Surfaces SIAM Journal on Numerical Analysis. ,vol. 47, pp. 3339- 3358 ,(2009) , 10.1137/080717602
André Massing, Mats G. Larson, Anders Logg, Marie E. Rognes, A Stabilized Nitsche Fictitious Domain Method for the Stokes Problem Journal of Scientific Computing. ,vol. 61, pp. 604- 628 ,(2014) , 10.1007/S10915-014-9838-9
Peter Hansbo, Mats G. Larson, Sara Zahedi, A cut finite element method for a Stokes interface problem Applied Numerical Mathematics. ,vol. 85, pp. 90- 114 ,(2014) , 10.1016/J.APNUM.2014.06.009
Erik Burman, Peter Hansbo, Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method Applied Numerical Mathematics. ,vol. 62, pp. 328- 341 ,(2012) , 10.1016/J.APNUM.2011.01.008
August Johansson, Mats G. Larson, A high order discontinuous Galerkin Nitsche method for elliptic problems with fictitious boundary Numerische Mathematik. ,vol. 123, pp. 607- 628 ,(2013) , 10.1007/S00211-012-0497-1
Maxim A. Olshanskii, Arnold Reusken, A finite element method for surface PDEs: matrix properties Numerische Mathematik. ,vol. 114, pp. 491- 520 ,(2009) , 10.1007/S00211-009-0260-4
Erik Burman, Peter Hansbo, Mats G. Larson, A stabilized cut finite element method for partial differential equations on surfaces: The Laplace–Beltrami operator Computer Methods in Applied Mechanics and Engineering. ,vol. 285, pp. 188- 207 ,(2015) , 10.1016/J.CMA.2014.10.044