2015
DOI: 10.1016/j.cma.2015.08.001
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Stabilized method of imposing Dirichlet boundary conditions using a recovered stress field

Abstract: -mail: manuel.tur@mcm.upv.es,jalbelda@mcm.upv.es,onmaral@upvnet.upv.es,jjrodena@mcm.upv.es Abstract This paper proposes a new formulation to impose Dirichlet boundary conditions on immersed boundary Cartesian Finite Element meshes. The method uses a recovered stress field calculated by Superconvergent Patch Recovery to stabilize the Lagrange multiplier formulation of the problem. The optimal convergence of the method and the convergence of the proposed iterative procedure are demonstrated. The proposed met… Show more

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Cited by 24 publications
(50 citation statements)
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References 37 publications
(81 reference statements)
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“…Stenberg [48] analyzes the approximation properties of the multiplier space used to impose the Dirichlet boundary conditions using the Nitsche method. From this analysis, if the solution is regular enough, the optimal convergence rate can be achieved [52] …”
Section: Lagrange Multiplier Interpolation: Penalty Methodsmentioning
confidence: 99%
See 4 more Smart Citations
“…Stenberg [48] analyzes the approximation properties of the multiplier space used to impose the Dirichlet boundary conditions using the Nitsche method. From this analysis, if the solution is regular enough, the optimal convergence rate can be achieved [52] …”
Section: Lagrange Multiplier Interpolation: Penalty Methodsmentioning
confidence: 99%
“…However, it is somewhat cumbersome to obtain an explicit formula for it, as its computation derives from equation (7). Following the ideas presented in [52], we propose an iterative process to solve the optimization problem 6 in which the stabilization term pN is assumed to be constant. After solving the problem, pN is updated from the finite element solution, and problem 6 is solved again.…”
Section: Iterative Solution Methodsmentioning
confidence: 99%
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