Meshless and Generalized Finite Element Methods: A Survey of Some Major Results

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Imposing essential boundary conditions in mesh-free methods (2004, methodology): “These techniques can be classified in two main groups: (1) methods based on a modification of the weak form, such as the Lagrange multiplier method [4], the penalty method [7] and Nitsche’s method [8,9], and (2) methods that can be interpreted as a modification of the interpolation shape functions, ”
Kernel techniques: From machine learning to meshless methods (2006, background): “The integration error can be quite serious (Ciarlet 1991, Babuška et al. 2002) and needs a careful selection of integration techniques.”
Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method (2012, methodology): “The penalty method in variational form [57,58] is based on the addition of a penalty term δWp to the geometrically nonlinear variational equation of the principle of virtual work Eq.”
Meshfree Methods: Progress Made after 20 Years (2017, unknown): “A general survey of mathematical results concerning PU methods has been provided (Babu š ka et al. 2003).”
The Finite Cell Method: A Review in the Context of Higher-Order Structural Analysis of CAD and Image-Based Geometric Models (2015, methodology): “The most popular approaches include the penalty method [8, 9, 55, 199], the Lagrange multiplier method [29, 55, 56, 58, 59, 61], and Nitsche’s method [17, 30, 43, 51, 64, 66, 147, 171].”