The variational collocation method

Canuto, 2006

Quarteroni, 2008

Schillinger, 2015, A collocated c0 finite element method: Reduced quadrature perspective, cost comparison with standard finite elements, and explicit structural dynamics, Internat. J. Numer. Methods Engrg., 102, 576, 10.1002/nme.4783

Hughes, 2005, Isogeometric analysis CAD, finite elements, NURBS, exact geometry and mesh refinement, Comput. Methods Appl. Mech. Engrg., 194, 4135, 10.1016/j.cma.2004.10.008

Cottrell, 2009

Bazilevs, 2010, Isogeometric analysis using T-splines, Comput. Methods Appl. Mech. Engrg., 199, 229, 10.1016/j.cma.2009.02.036

Gomez, 2008, Isogeometric analysis of the Cahn–Hilliard phase-field model, Comput. Methods Appl. Mech. Engrg., 197, 4333, 10.1016/j.cma.2008.05.003

Gomez, 2010, Isogeometric analysis of the isothermal Navier–Stokes–Korteweg equations, Comput. Methods Appl. Mech. Engrg., 199, 1828, 10.1016/j.cma.2010.02.010

Lipton, 2010, Robustness of isogeometric structural discretizations under severe mesh distortion, Comput. Methods Appl. Mech. Engrg., 199, 357, 10.1016/j.cma.2009.01.022

Evans, 2013, Isogeometric divergence-conforming B-splines for the unsteady Navier–Stokes equations, J. Comput. Phys., 241, 141, 10.1016/j.jcp.2013.01.006

Auricchio, 2010, Isogeometric collocation methods, Math. Models Methods Appl. Sci., 20, 2075, 10.1142/S0218202510004878

Auricchio, 2012, Isogeometric collocation for elastostatics and explicit dynamics, Comput. Methods Appl. Mech. Engrg., 249, 2, 10.1016/j.cma.2012.03.026

Casquero, 2016, Isogeometric collocation using analysis-suitable t-splines of arbitrary degree, Comput. Methods Appl. Mech. Engrg., 301, 164, 10.1016/j.cma.2015.12.014

Gomez, 2014, Accurate, efficient, and (iso)geometrically flexible collocation methods for phase-field models, J. Comput. Phys., 262, 153, 10.1016/j.jcp.2013.12.044

Reali, 2015, An isogeometric collocation approach for Bernoulli–Euler beams and kirchhoff plates, Comput. Methods Appl. Mech. Engrg., 284, 623, 10.1016/j.cma.2014.10.027

Casquero, 2016, A hybrid variational-collocation immersed method for fluid–structure interaction using unstructured T-splines, Internat. J. Numer. Methods Engrg., 105, 855, 10.1002/nme.5004

De~Lorenzis, 2015, Isogeometric collocation: Neumann boundary conditions and contact, Comput. Methods Appl. Mech. Engrg., 284, 21, 10.1016/j.cma.2014.06.037

Kruse, 2015, Isogeometric collocation for large deformation elasticity and frictional contact problems, Comput. Methods Appl. Mech. Engrg., 296, 73, 10.1016/j.cma.2015.07.022

Schillinger, 2013, Isogeometric collocation: Cost comparison with Galerkin methods and extension to adaptive hierarchical NURBS discretizations, Comput. Methods Appl. Mech. Engrg., 267, 170, 10.1016/j.cma.2013.07.017

Arroyo, 2006, Local maximum-entropy approximation schemes: a seamless bridge between finite elements and meshfree methods, Internat. J. Numer. Methods Engrg., 65, 2167, 10.1002/nme.1534

Hobson, 1907

T.J.R. Hughes, The Finite Element Method: Linear Static and Dynamic Finite Element Analysis Cited By (since 1996), 1023.

Li, 2007

Kiendl, 2009, Isogeometric shell analysis with Kirchhoff–Love elements, Comput. Methods Appl. Mech. Engrg., 198, 3902, 10.1016/j.cma.2009.08.013

Elguedj, 2008, B¯ and F¯ projection methods for nearly incompressible linear and non-linear elasticity and plasticity using higher-order NURBS elements, Comput. Methods Appl. Mech. Engrg., 197, 2732, 10.1016/j.cma.2008.01.012

Auricchio, 2007, A fully locking-free isogeometric approach for plane linear elasticity problems: a stream function formulation, Comput. Methods Appl. Mech. Engrg., 197, 160, 10.1016/j.cma.2007.07.005

Dimitri, 2014, NURBS and T-spline-based isogeometric cohesive zone modeling of interface debonding, Comput. Mech., 54, 369, 10.1007/s00466-014-0991-7

Dhote, 2015, Shape memory alloy nanostructures with coupled dynamic thermo-mechanical effects, Comput. Phys. Comm.

Dhote, 2013, Isogeometric analysis of a dynamic thermo-mechanical phase-field model applied to shape memory alloys, Comput. Mech., 53, 1235, 10.1007/s00466-013-0966-0

Bazilevs, 2007, Variational multiscale residual-based turbulence modeling for large eddy simulation of incompressible flows, Comput. Methods Appl. Mech. Engrg., 197, 173, 10.1016/j.cma.2007.07.016

Gomez, 2013, Three-dimensional simulation of unstable gravity-driven infiltration of water into a porous medium, J. Comput. Phys., 238, 217, 10.1016/j.jcp.2012.12.018

Liu, 2015, Liquid–vapor phase transition: Thermomechanical theory, entropy stable numerical formulation, and boiling simulations, Comput. Methods Appl. Mech. Engrg., 297, 476, 10.1016/j.cma.2015.09.007

Ambati, 2015, A review on phase-field models of brittle fracture and a new fast hybrid formulation, Comput. Mech., 55, 383, 10.1007/s00466-014-1109-y

Gomez, 2012, An unconditionally energy-stable method for the phase field crystal equation, Comput. Methods Appl. Mech. Engrg., 249, 52, 10.1016/j.cma.2012.03.002

Liu, 2013, Functional entropy variables: a new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier–Stokes–Korteweg equations, J. Comput. Phys., 248, 47, 10.1016/j.jcp.2013.04.005

Dimitri, 2014, Isogeometric large deformation frictionless contact using t-splines, Comput. Methods Appl. Mech. Engrg., 269, 394, 10.1016/j.cma.2013.11.002

De~Lorenzis, 2012, A mortar formulation for 3D large deformation contact using NURBS-based isogeometric analysis and the augmented Lagrangian method, Comput. Mech., 49, 1, 10.1007/s00466-011-0623-4

Vilanova, 2013, Capillary networks in tumor angiogenesis: From discrete endothelial cells to phase-field averaged descriptions via isogeometric analysis, Int. J. Numer. Methods Biomed. Eng., 29, 1015, 10.1002/cnm.2552

Vilanova, 2013, Coupling of discrete random walks and continuous modeling for three-dimensional tumor-induced angiogenesis, Comput. Mech., 53, 449, 10.1007/s00466-013-0958-0

Bazilevs, 2008, Isogeometric fluid–structure interaction: Theory, algorithms, and computations, Comput. Mech., 43, 3, 10.1007/s00466-008-0315-x

Kamensky, 2015, An immersogeometric variational framework for fluid–structure interaction: Application to bioprosthetic heart valves, Comput. Methods Appl. Mech. Engrg., 284, 1005, 10.1016/j.cma.2014.10.040

Bueno, 2014, Interaction of complex fluids and solids: theory, algorithms and application to phase-change-driven implosion, Comput. Mech., 1

Casquero, 2015, A NURBS-based immersed methodology for fluid–structure interaction, Comput. Methods Appl. Mech. Engrg., 284, 943, 10.1016/j.cma.2014.10.055

Babuška, 1996, Computer-based proof of the existence of superconvergence points in the finite element method; superconvergence of the derivatives in finite element solutions of Laplace’s, Poisson’s, and the elasticity equations, Numer. Methods Partial Differential Equations, 12, 347, 10.1002/num.1690120303

Barlow, 1976, Optimal stress locations in finite element models, Internat. J. Numer. Methods Engrg., 10, 243, 10.1002/nme.1620100202

Babuška, 2007, Superconvergence in the generalized finite element method, Numer. Math., 107, 353, 10.1007/s00211-007-0096-8

Wahlbin, 1995

Anitescu, 2015, An isogeometric collocation method using superconvergent points, Comput. Methods Appl. Mech. Engrg., 284, 1073, 10.1016/j.cma.2014.11.038

Bazilevs, 2010, Isogeometric analysis using t-splines, Comput. Methods Appl. Mech. Engrg., 199, 229, 10.1016/j.cma.2009.02.036

Beirao~da Veiga, 2013, Analysis suitable T-splines of arbitrary degree: Definition, linear independence, and approximation properties, Math. Models Methods Appl. Sci., 23, 1979, 10.1142/S0218202513500231

J. Simo, K. Pister, Remarks on rate constitutive equations for finite deformation 46 (1984) 201–215.

Reali, 2015, An isogeometric collocation approach for Bernoulli–Euler beams and Kirchhoff plates, Comput. Methods Appl. Mech. Engrg., 284, 623, 10.1016/j.cma.2014.10.027

Schillinger, 2014, Reduced Bézier element quadrature rules for quadratic and cubic splines in isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 277, 1, 10.1016/j.cma.2014.04.008

Hughes, 2010, Efficient quadrature for nurbs-based isogeometric analysis, Comput. Methods Appl. Mech. Engrg., 199, 301, 10.1016/j.cma.2008.12.004

C. De Boor, A practical guide to splines, Math. Comput.

de~Boor, 2005, Divided differences, Surv. Approx. Theory, 1, 46