A unified approach for embedded boundary conditions for fourth-order elliptic problems
Summary An efficient procedure for embedding kinematic boundary conditions in the biharmonic equation, for problems such as the pure streamfunction formulation of the Navier–Stokes equations and thin plate bending, is based on a stabilized variational formulation, obtained by Nitsche's approach...
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Published in | International journal for numerical methods in engineering Vol. 104; no. 7; pp. 655 - 675 |
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Main Authors | , |
Format | Journal Article |
Language | English |
Published |
Bognor Regis
Blackwell Publishing Ltd
16.11.2015
Wiley Subscription Services, Inc |
Subjects | |
Online Access | Get full text |
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Summary: | Summary
An efficient procedure for embedding kinematic boundary conditions in the biharmonic equation, for problems such as the pure streamfunction formulation of the Navier–Stokes equations and thin plate bending, is based on a stabilized variational formulation, obtained by Nitsche's approach for enforcing boundary constraints. The absence of kinematic admissibility constraints allows the use of non‐conforming meshes with non‐interpolatory approximations, thereby providing added flexibility in addressing the higher continuity requirements typical of these problems. Variationally conjugate pairs weakly enforce kinematic boundary conditions. The use of a scaling factor leads to a formulation with a single stabilization parameter. For plates, the enforcement of tangential derivatives of deflections obviates the need for pointwise enforcement of corner values in the presence of corners. The single stabilization parameter is determined from a local generalized eigenvalue problem, guaranteeing coercivity of the discrete bilinear form. The accuracy of the approach is verified by representative computations with bicubic B‐splines, providing guidance to the determination of the scaling and exhibiting optimal rates of convergence and robust performance with respect to values of the stabilization parameter. Copyright © 2014 John Wiley & Sons, Ltd. |
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Bibliography: | ark:/67375/WNG-6SFMFFW8-5 istex:25EC5167EE39D0E54D92E0588CEA744603B1DED8 ArticleID:NME4813 ObjectType-Article-1 SourceType-Scholarly Journals-1 ObjectType-Feature-2 content type line 23 |
ISSN: | 0029-5981 1097-0207 |
DOI: | 10.1002/nme.4813 |