An unfitted finite element method using discontinuous Galerkin

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Small and large deformation analysis with the p- and B-spline versions of the Finite Cell Method (2012, methodology): “The best approximation property to the total strain energy U states that the solution of a Galerkin finite element scheme represents a least-squares best fit to the exact solution in terms of Eq.”
The non-symmetric Nitsche method for the parameter-free imposition of weak boundary and coupling conditions in immersed finite elements (2016, methodology): “Here, we employ definitions (9) and (10) to general discretizations of K, including unfitted meshes with finite elements whose boundaries do not conform to ∂K [11, 34, 75].”
The hp‐d‐adaptive finite cell method for geometrically nonlinear problems of solid mechanics (2012, methodology): “The best approximation property to the total strain energy states that the solution of a Galerkin FE scheme represents a least-squares best fit to the exact solution in terms of Equation (8) [2, 47].”
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”