A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes
By Joan Baiges, Ramon Codina, F. Henke, S. Shahmiri, Wolfgang A. Wall. 2012
86 citations recorded by the source corpus.
In this paper, we propose a way to weakly prescribe Dirichlet boundary conditions in embedded finite element meshes. The key feature of the method is that the algorithmic parameter of the formulation which allows to ensure stability is independent of the numerical approximation, relatively small, and can be fixed a priori. Moreover, the formulation is symmetric for symmetric problems. An additional element‐discontinuous stress field is used to enforce the boundary conditions in the Poisson problem. Additional terms are required in order to guarantee stability in the convection–diffusion equation and the Stokes problem. The proposed method is then easily extended to the transient Navier–Stokes equations. Copyright © 2012 John Wiley & Sons, Ltd.
Subfields: Computational Mechanics
View Paper: https://www.semanticscholar.org/paper/3951ef08963b5161d80baf5ac4cbb4c1f78ba115
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Citations in the corpus
- A Cut Finite Element Method with Boundary Value Correction for the Incompressible Stokes Equations (2017, methodology): “…D¨uster, et al. [14,23]; the least squares stabilized Lagrange multiplier methods of Haslinger and Renard [18], Tur et al. [25], and Baiges et al. [2]; the stabilization of Nitsche’s method by Codina and Baiges [12]; the local projection stabilization of multipliers of Barrenechea and Chouly [3]…”
- The non-symmetric Nitsche method for the parameter-free imposition of weak boundary and coupling conditions in immersed finite elements (2016, methodology): “Therefore, there has been an increasing interest in methods that can enforce boundary and interface conditions without mesh dependent stabilization parameters [9, 23, 44, 48].”
- The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models (2015, methodology): “Some examples include the immersed boundary method due to Peskin [121], certain versions of the extended finite elemen t method [21, 68, 96, 106, 148, 167, 172], fixed-grid methods in fluid-structure interaction [10,58,134,136,184,186,1 96], isogeometric immersed boundary methods [86, 87, 94, 133, 1”