A discontinuous‐Galerkin‐based immersed boundary method

By Adrian J. Lew, Gustavo C. Buscaglia. 2008

134 citations recorded by the source corpus.

Subfields: Computational Mechanics, Mechanics of Materials

View Paper: https://www.semanticscholar.org/paper/170a186bd762036833f105a127f66c5e8777dc98

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In Computational Mechanics

In Mechanics of Materials

Citations in the corpus

On methods for stabilizing constraints over enriched interfaces in elasticity (2009, methodology): “The challenge of enforcing constraints across an internal discontinuity produced by an enriched solution field has some similarities to the numerics of other problems, including enforcing Dirichlet constraints on an enriched field and enforcing continuity constraints in meshfree, discontinuous enric”
An embedded Dirichlet formulation for 3D continua (2010, unknown): “in [3, 9], bubblestabilized methods [10–12], variations of Nitsche’s method [13–18] or hybrid and discontinuous Galerkin methods [17, 19, 20].”
An improved finite element space for discontinuous pressures (2010, background): “A rigorous proof of the interpolation 21 estimate has been undertaken by Agouzal and Buscaglia, of which some preliminary results have already been communicated [27] and a complete version is in preparation.”
CutFEM: Discretizing geometry and partial differential equations (2015, methodology): “Other related approaches based on Lagrange multipliers or discontinuous Galerkin methods have been suggested in the following works [14–20].”
A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes (2012, methodology): “A DG-based immersed boundary method is proposed in [25], which consists of switching elements intersected by the boundary to a DG approximation and imposing the Dirichlet boundary conditions strongly.”
Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods (2012, background): “This can have an adverse effect on the conditioning of the system for quasi-static problems as previously reported (see Lew and Buscaglia [22] and Embar et al.”
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”
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].”
A geometric mass‐preserving redistancing scheme for the level set function (2011, background): “In fact, the space of level set functions that share the same given interface is extremely small [31] and it is likely that none of its elements provides a reasonable approximation to the distance function.”
Robust imposition of Dirichlet boundary conditions on embedded surfaces (2012, background): “Although we did not encounter any numerical issues in the numerical examples reported in Section 5, we do acknowledge that, for the sake of robustness, techniques that snap the surface to a vertex when it is too close (as in Lew and Buscaglia [14]) or the employment of other tolerancing schemes as i”