A finite element method for domain decomposition with non-matching grids

By Roland Becker, Peter Hansbo, Rolf Stenberg. 2003

277 citations recorded by the source corpus.

Subfields: Computational Mechanics, Computational Theory and Mathematics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/eb773e0db45e3920fbfea4bbcd7f19915a7ae2c7

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Computational Mechanics

In Computational Theory and Mathematics

In Mechanics of Materials

Citations in the corpus

A FINITE ELEMENT METHOD ON COMPOSITE GRIDS BASED ON NITSCHE'S METHOD (2003, methodology): “Our method stems from the work of Nitsche [12], where a method for consistent weak enforcement of Dirichlet boundary conditions was introduced, and is related, in particular, to Becker, Hansbo and Stenberg [2], where the meshes were assumed to be non-matching on the interface but shape regular on bo”
A mixed finite element method for Darcy flow in fractured porous media with non-matching grids (2012, background): “[5, 6, 14] that focus on the elasticity problem in domains with fractures.”
A robust a-posteriori error estimator for discontinuous Galerkin methods for convection--diffusion equations (2009, background): “For L(2)-norm and functional error estimation, we also mention [8,14,20,26] and the references therein.”
A unified stabilized method for Stokes' and Darcy's equations (2007, methodology): “Moreover we discussed the possible extension to higher order finite elements and the coupling of the two systems using a Nitsche–type method.”
Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems (2001, methodology): “Finally, Becker and Hansbo [17] and Dutra do Carmo and Duarte [48] recently used the IP approach as a way of dealing with nonmatching grids for domain decomposition.”
Stabilization of explicit coupling in fluid-structure interaction involving fluid incompressibility (2009, methodology): “Extensions to the non-linear case of some of the coupling strategies introduced in this paper are provided in paragraph §5.5.”
A stabilized Lagrange multiplier method for the enriched finite-element approximation of contact problems of cracked elastic bodies (2012, methodology): “This method has also been extended to interface problems on non-matching meshes in [6, 19] and more recently for bilateral (linear) contact problems in [22] and for contact problems in elastostatics [25].”
An adaptation of Nitscheʼs method to the Tresca friction problem (2014, background): “[37] for the Dirichlet problem, [7] for do-”
ENERGY NORM A POSTERIORI ERROR ESTIMATION OF hp-ADAPTIVE DISCONTINUOUS GALERKIN METHODS FOR ELLIPTIC PROBLEMS (2007, methodology): “While the proof of the energy norm a posteriori error bounds in [ 7 ] hinges on a saturation assumption on the finite element spaces, the analyses in [6, 8, 20] are based on exploiting suitable Helmholtz decompositions of the error, together with the local conservation properties of the underlying D”
Estimation of penalty parameters for symmetric interior penalty Galerkin methods (2007, methodology): “The analysis and application of SIPG to a wide range of problems can be found in the literature: a non-exhaustive list is given in [7,8,10,14,20,22,23,17] and the references herein.”
A comparison of mortar and Nitsche techniques for linear elasticity (2004, methodology): “To prove the first a priori estimate, we follow an idea presented in [BH99] for the Laplace operator.”