Annavarapu C, Hautefeuille M, Dolbow J (2012) A robust Nitsche’s formulation for interface problems. Comput Methods Appl Mech Eng 228:44–54
Annavarapu C, Hautefeuille M, Dolbow J (2012) Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods. Int J Numer Methods Eng 92(2):206–228
Annavarapu C, Hautefeuille M, Dolbow J (2013) A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part II: intersecting interfaces. Comput Methods Appl Mech Eng 267:318–341
[+]
Annavarapu C, Hautefeuille M, Dolbow J (2012) A robust Nitsche’s formulation for interface problems. Comput Methods Appl Mech Eng 228:44–54
Annavarapu C, Hautefeuille M, Dolbow J (2012) Stable imposition of stiff constraints in explicit dynamics for embedded finite element methods. Int J Numer Methods Eng 92(2):206–228
Annavarapu C, Hautefeuille M, Dolbow J (2013) A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part II: intersecting interfaces. Comput Methods Appl Mech Eng 267:318–341
Annavarapu C, Hautefeuille M, Dolbow J (2014) A Nitsche stabilized finite element method for frictional sliding on embedded interfaces. Part I: single interface. Comput Methods Appl Mech Eng 268:417–436
Baiges J, Codina R, Henke F, Shahmiri S, Wall WA (2012) A symmetric method for weakly imposing Dirichlet boundary conditions in embedded finite element meshes. Int J Numer Methods Eng 90(5):636–658
Barbosa HJC, Hughes TJR (1992) Circumventing the Babuska–Brezzi condition in mixed finite element approximations of elliptic variational inequalities. Comput Methods Appl Mech Eng 97(2):193–210
Bechet E, Moes N, Wohlmuth B (2009) A stable Lagrange multiplier space for stiff interface conditions within the extended finite element method. Int J Numer Methods Eng 78(8):931–954
Belgacem F, Hild P, Laborde P (1998) The mortar finite element method for contact problems. Math Comput Model 28(4–8):263–271
Brezzi F (1974) On the existence, uniqueness and approximation of saddle-point problems arising from Lagrangian multipliers. ESAIM 8(R2):129–151
Brezzi F, Fortin M (1991) Mixed and hybrid finite element methods. Springer, New York
Burman E, Hansbo P (2010) Fictitious domain finite element methods using cut elements: I. A stabilized Lagrange multiplier method. Comput Methods Appl Mech Eng 199:2680–2686
Burman E, Hansbo P (2012) Fictitious domain finite element methods using cut elements: II. A stabilized Nitsche method. Appl Numer Math 62(4):328–341
Chouly F, Hild P, Renard Y (2013) Symmetric and non-symmetric variants of Nitsche’s method for contact problems in elasticity: theory and numerical experiments. doi: 10.1007/s00466-012-0780-0
Codina R, Baiges J (2009) Approximate imposition of boundary conditions in immersed boundary methods. Int J Numer Methods Eng 80(11):1379–1405
Coorevits P, Hild P, Lhalouani K, Sassi T (2001) Mixed finite element methods for unilateral problems: convergence analysis and numerical studies. Math Comput 71(237):1–25
ElAbbasi N, Bathe KJ (2001) Stability and patch test performance of contact discretizations and a new solution algorithm. Comput Struct 79:1473–1486
Fischer K, Wriggers P (2005) Frictionless 2D contact formulations for finite deformations based on the mortar method. Comput Mech 36:226–244
Fischer K, Wriggers P (2005) Mortar based frictional contact formulation for higher order interpolations using the moving friction cone. Comput Methods Appl Mech Eng 195:5020–5036
Gerstenberger A, Wall WA (2010) An embedded Dirichlet formulation for 3D continua. Int J Numer Methods Eng 82(5):537–563
Gitterle M, Popp A, Gee MW, Wall WA (2010) A dual mortar approach for 3D finite deformation contact with consistent linearization. Int J Numer Methods Eng 84(5):543–571
Gravouil A, Pierres E, Baietto M (2011) Stabilized global-local X-FEM for 3D non-planar frictional contact using relevant meshes. Int J Numer Methods Eng 88(13):1449–1475
Hammer ME (2013) Frictional mortar contact for finite deformation problems with synthetic contact kinematics. Comput Mech 51(6):975–998
Hansbo P, Lovadina C, Perugia I, Sangalli G (2005) A Lagrange multiplier method for the finite element solution of elliptic interface problems using non-matching meshes. Numer Math 100:91– 115
Hartmann S, Ramm E (2008) A mortar based contact formulation for non-linear dynamics using dual Lagrange multipliers. Finite Elem Anal Des 44:245–258
Haslinger J, Renard Y (2009) A new fictitious domain approach inspired by the extended finite element method. SIAM J Numer Anal 47(2):1474–1499. doi: 10.1137/070704435
Heintz P, Hansbo P (2006) Stabilized Lagrange multiplier methods for bilateral contact with friction. Comput Methods Appl Mech Eng 195:4323–4333
Hild P (2000) Numerical implementation of two nonconforming finite element methods for unilateral contact. Comput Methods Appl Mech Eng 184:99–123
Hild P, Laborde P (2002) Quadratic finite element methods for unilaterial contact problems. Appl Numer Math 41:401–421
Hild P, Renard Y (2010) A stabilized Lagrange multiplier method for the finite element approximation of contact problems in elastostatics. Numer Math 115(101–129):2456–2471
Hueber S, Mair M, Wohlmuth B (2005) A priori error estimates and an inexact primal-dual active set strategy for linear and quadratic finite elements applied to multibody contact problems. Appl Numer Math 54:555–576
Hueber S, Stadler G, Wohlmuth BI (2008) A primal-dual active set algorithm for three-dimensional contact problems with coulomb friction. SIAM J Sci Comput 30(2):572–596
Hueber S, Wohlmuth B (2005) A primal-dual active set strategy for non-linear multibody contact problems. Comput Methods Appl Mech Eng 194:3147–3166
Laursen T (2002) Computational contact and impact mechanics. Springer, Berlin
Liu F, Borja RI (2010) Stabilized low-order finite elements for frictional contact with the extended finite element method. Comput Methods Appl Mech Eng 199(37–40):2456–2471
McDevitt T, Laursen T (2000) A mortar-finite element formulation for frictional contact problems. Int J Numer Methods Eng 48:1525–1547
Nadal E, Ródenas JJ, Albelda J, Tur M, Tarancón JE, Fuenmayor FJ (2013) Efficient finite element methodology based on cartesian grids: application to structural shape optimization. Abstr Appl Anal, pp 1–19
Nistor I, Guiton M, Massin P, Moes N, Geniaut S (2009) An X-FEM approach for large sliding contact along discontinuities. Int J Numer Meth Eng 78(12):1407–1435
Popp A, Gitterle M, Gee MW, Wall WA (2010) Finite deformation frictional mortar contact using a semi-smooth Newton method with consistent linearization. Int J Numer Methods Eng 83(11):1428–1465
Puso M (2004) A 3D mortar method for solid mechanics. Int J Numer Methods Eng 59:315–336
Puso M, Laursen T (2004) A mortar segment-to-segment contact method for large deformation solid mechanics. Comput Methods Appl Mech Eng 193:601–629
Puso M, Laursen T (2004) A mortar segment-to-segment frictional contact method for large deformations. Comput Methods Appl Mech Eng 193:4891–4913
Puso M, Laursen T, Solberg J (2008) A segment-to-segment mortar contact method for quadratic elements and large deformations. Comput Methods Appl Mech Eng 197:555–566
Ródenas J, Tur M, Fuenmayor F, Vercher A (2007) Improvement of the superconvergent patch recovery technique by the use of constraint equations: the SPR-C technique. Int J Numer Methods Eng 70:705–727
Saad Y (2003) Iterative methods for sparse linear systems., Applied Mathematical SciencesSociety for Industrial and Applied Mathematics, Philadelphia
Sanders JD, Laursen TA, Puso M (2012) A Nitsche embedded mesh method. Comput Mech 49:243–257
Schott B, Wall W (2014) A new face-oriented stabilized XFEM approach foir 2D and 3D incompressible Navier–Stokes equations. Comput Methods Appl Mech Eng 276:233–265
Simo J, Wriggers P, Taylor R (1985) A perturbed Lagrangian formulation for the finite element solution of contact problems. Comput Methods Appl Mech Eng 50:163–180
Stenberg R (1995) On some techniques for approximating boundary conditions in the finite element method. J Comput Appl Math 63:139–148
Strouboulis T, Copps K, Babuška I (2000) The generalized finite element method: an example of its implementation and illustration of its performance. Int J Numer Methods Eng 47:1401–1417
Tur M, Fuenmayor F, Wriggers P (2009) A mortar-based frictional contact formulation for large deformations using Lagrange multipliers. Comput Methods Appl Mech Eng 198:2860–2873
Tur M, Albelda J, Nadal E, Ródenas JJ (2014) Imposing Dirichlet boundary conditions in hierarchical Cartesian meshes by means of stabilized Lagrange multipliers. Int J Numer Methods Eng 98(6):399–417
Tur M, Albelda J, Marco O, Ródenas JJ (2014) Stabilized method to impose Dirichlet boundary conditions using a smooth stress field. Comput Methods Appl M, Under review
Wohlmuth B, Popp A, Gee MW, Wall WA (2012) An abstract framework for a priori estimates for contact problems in 3d with quadratic finite elements. Comput Mech 49:735–747
Wriggers P (2002) Computational contact mechanics. Wiley, Chichester
Yang B, Laursen T, Meng X (2005) Two dimensional mortar contact methods for large deformation frictional sliding. Int J Numer Methods Eng 62:1183–1225
Zavarise G, Wriggers P (1998) A segment-to-segment contact strategy. Mathe Comput Model 28(4–8):497–515
Zavarise G, Wriggers P (2008) A formulation for frictionless contact problems using a weak form introduced by Nitsche. Comput Mech 41:407–420
Zavarise G, De Lorenzis L (2009) A modified node-to-segment algorithm passing the contact patch test. Int J Numer Methods Eng 79:379–416
Zienkiewicz O, Zhu J (1992) Superconvergent patch recovery techniques and a posteriori error estimation., Part I: the recovery technique. Int J Numer Methods Eng 33:1331–1364
[-]