Moés, N., Dolbow, J., & Belytschko, T. (1999). A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 46(1), 131-150. doi:10.1002/(sici)1097-0207(19990910)46:1<131::aid-nme726>3.0.co;2-j
Sukumar, N., & Prévost, J.-H. (2003). Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation. International Journal of Solids and Structures, 40(26), 7513-7537. doi:10.1016/j.ijsolstr.2003.08.002
Strouboulis, T., Copps, K., & Babuška, I. (2001). The generalized finite element method. Computer Methods in Applied Mechanics and Engineering, 190(32-33), 4081-4193. doi:10.1016/s0045-7825(01)00188-8
[+]
Moés, N., Dolbow, J., & Belytschko, T. (1999). A finite element method for crack growth without remeshing. International Journal for Numerical Methods in Engineering, 46(1), 131-150. doi:10.1002/(sici)1097-0207(19990910)46:1<131::aid-nme726>3.0.co;2-j
Sukumar, N., & Prévost, J.-H. (2003). Modeling quasi-static crack growth with the extended finite element method Part I: Computer implementation. International Journal of Solids and Structures, 40(26), 7513-7537. doi:10.1016/j.ijsolstr.2003.08.002
Strouboulis, T., Copps, K., & Babuška, I. (2001). The generalized finite element method. Computer Methods in Applied Mechanics and Engineering, 190(32-33), 4081-4193. doi:10.1016/s0045-7825(01)00188-8
Strouboulis, T., Zhang, L., & Babuška, I. (2006). Assessment of the cost and accuracy of the generalized FEM. International Journal for Numerical Methods in Engineering, 69(2), 250-283. doi:10.1002/nme.1750
Melenk, J. M., & Babuška, I. (1996). The partition of unity finite element method: Basic theory and applications. Computer Methods in Applied Mechanics and Engineering, 139(1-4), 289-314. doi:10.1016/s0045-7825(96)01087-0
Stolarska, M., Chopp, D. L., Moës, N., & Belytschko, T. (2001). Modelling crack growth by level sets in the extended finite element method. International Journal for Numerical Methods in Engineering, 51(8), 943-960. doi:10.1002/nme.201
Moumnassi, M., Belouettar, S., Béchet, É., Bordas, S. P. A., Quoirin, D., & Potier-Ferry, M. (2011). Finite element analysis on implicitly defined domains: An accurate representation based on arbitrary parametric surfaces. Computer Methods in Applied Mechanics and Engineering, 200(5-8), 774-796. doi:10.1016/j.cma.2010.10.002
Legrain, G., Chevaugeon, N., & Dréau, K. (2012). High order X-FEM and levelsets for complex microstructures: Uncoupling geometry and approximation. Computer Methods in Applied Mechanics and Engineering, 241-244, 172-189. doi:10.1016/j.cma.2012.06.001
Burman, E., & Hansbo, P. (2010). Fictitious domain finite element methods using cut elements: I. A stabilized Lagrange multiplier method. Computer Methods in Applied Mechanics and Engineering, 199(41-44), 2680-2686. doi:10.1016/j.cma.2010.05.011
HEIKKOLA, E., KUZNETSOV, Y. A., & LIPNIKOV, K. N. (1999). FICTITIOUS DOMAIN METHODS FOR THE NUMERICAL SOLUTION OF THREE-DIMENSIONAL ACOUSTIC SCATTERING PROBLEMS. Journal of Computational Acoustics, 07(03), 161-183. doi:10.1142/s0218396x99000126
Hetmaniuk, U., & Farhat, C. (2003). A finite element-based fictitious domain decomposition method for the fast solution of partially axisymmetric sound-hard acoustic scattering problems. Finite Elements in Analysis and Design, 39(8), 707-725. doi:10.1016/s0168-874x(03)00055-6
Farhat, C., & Hetmaniuk, U. (2002). A fictitious domain decomposition method for the solution of partially axisymmetric acoustic scattering problems. Part I: Dirichlet boundary conditions. International Journal for Numerical Methods in Engineering, 54(9), 1309-1332. doi:10.1002/nme.461
Ye, T., Mittal, R., Udaykumar, H. S., & Shyy, W. (1999). An Accurate Cartesian Grid Method for Viscous Incompressible Flows with Complex Immersed Boundaries. Journal of Computational Physics, 156(2), 209-240. doi:10.1006/jcph.1999.6356
Jahangirian, A., & Shoraka, Y. (2008). Adaptive unstructured grid generation for engineering computation of aerodynamic flows. Mathematics and Computers in Simulation, 78(5-6), 627-644. doi:10.1016/j.matcom.2008.04.004
Silva Santos, C. M., & Greaves, D. M. (2007). Using hierarchical Cartesian grids with multigrid acceleration. International Journal for Numerical Methods in Engineering, 69(8), 1755-1774. doi:10.1002/nme.1844
Jang, G.-W., Kim, Y. Y., & Choi, K. K. (2004). Remesh-free shape optimization using the wavelet-Galerkin method. International Journal of Solids and Structures, 41(22-23), 6465-6483. doi:10.1016/j.ijsolstr.2004.05.010
Mäkinen, R. A. E., Rossi, T., & Toivanen, J. (2000). A moving mesh fictitious domain approach for shape optimization problems. ESAIM: Mathematical Modelling and Numerical Analysis, 34(1), 31-45. doi:10.1051/m2an:2000129
Victoria, M., Querin, O. M., & Martí, P. (2010). Topology design for multiple loading conditions of continuum structures using isolines and isosurfaces. Finite Elements in Analysis and Design, 46(3), 229-237. doi:10.1016/j.finel.2009.09.003
Parussini, L., & Pediroda, V. (2009). Fictitious Domain approach with hp-finite element approximation for incompressible fluid flow. Journal of Computational Physics, 228(10), 3891-3910. doi:10.1016/j.jcp.2009.02.019
Bishop, J. (2003). Rapid stress analysis of geometrically complex domains using implicit meshing. Computational Mechanics, 30(5-6), 460-478. doi:10.1007/s00466-003-0424-5
Zhang, L., Gerstenberger, A., Wang, X., & Liu, W. K. (2004). Immersed finite element method. Computer Methods in Applied Mechanics and Engineering, 193(21-22), 2051-2067. doi:10.1016/j.cma.2003.12.044
Roma, A. M., Peskin, C. S., & Berger, M. J. (1999). An Adaptive Version of the Immersed Boundary Method. Journal of Computational Physics, 153(2), 509-534. doi:10.1006/jcph.1999.6293
García‐Ruíz, M. J., & Steven, G. P. (1999). Fixed grid finite elements in elasticity problems. Engineering Computations, 16(2), 145-164. doi:10.1108/02644409910257430
Daneshmand, F., & Kazemzadeh-Parsi, M. J. (2009). Static and dynamic analysis of 2D and 3D elastic solids using the modified FGFEM. Finite Elements in Analysis and Design, 45(11), 755-765. doi:10.1016/j.finel.2009.06.003
Bordas, S. P. A., Rabczuk, T., Hung, N.-X., Nguyen, V. P., Natarajan, S., Bog, T., … Hiep, N. V. (2010). Strain smoothing in FEM and XFEM. Computers & Structures, 88(23-24), 1419-1443. doi:10.1016/j.compstruc.2008.07.006
Simpson, R. N., Bordas, S. P. A., Trevelyan, J., & Rabczuk, T. (2012). A two-dimensional Isogeometric Boundary Element Method for elastostatic analysis. Computer Methods in Applied Mechanics and Engineering, 209-212, 87-100. doi:10.1016/j.cma.2011.08.008
Scott, M. A., Simpson, R. N., Evans, J. A., Lipton, S., Bordas, S. P. A., Hughes, T. J. R., & Sederberg, T. W. (2013). Isogeometric boundary element analysis using unstructured T-splines. Computer Methods in Applied Mechanics and Engineering, 254, 197-221. doi:10.1016/j.cma.2012.11.001
Hughes, T. J. R., Cottrell, J. A., & Bazilevs, Y. (2005). Isogeometric analysis: CAD, finite elements, NURBS, exact geometry and mesh refinement. Computer Methods in Applied Mechanics and Engineering, 194(39-41), 4135-4195. doi:10.1016/j.cma.2004.10.008
Zienkiewicz, O. C., & Zhu, J. Z. (1987). A simple error estimator and adaptive procedure for practical engineerng analysis. International Journal for Numerical Methods in Engineering, 24(2), 337-357. doi:10.1002/nme.1620240206
Zienkiewicz, O. C., & Zhu, J. Z. (1992). The superconvergent patch recovery anda posteriori error estimates. Part 1: The recovery technique. International Journal for Numerical Methods in Engineering, 33(7), 1331-1364. doi:10.1002/nme.1620330702
Wiberg, N.-E., Abdulwahab, F., & Ziukas, S. (1994). Enhanced superconvergent patch recovery incorporating equilibrium and boundary conditions. International Journal for Numerical Methods in Engineering, 37(20), 3417-3440. doi:10.1002/nme.1620372003
Blacker, T., & Belytschko, T. (1994). Superconvergent patch recovery with equilibrium and conjoint interpolant enhancements. International Journal for Numerical Methods in Engineering, 37(3), 517-536. doi:10.1002/nme.1620370309
Ramsay, A. C. A., & Maunder, E. A. W. (1996). Effective error sttimation from continous, boundary admissible estimated stress fields. Computers & Structures, 61(2), 331-343. doi:10.1016/0045-7949(96)00034-x
Ródenas, J. J., Tur, M., Fuenmayor, F. J., & Vercher, A. (2007). Improvement of the superconvergent patch recovery technique by the use of constraint equations: the SPR-C technique. International Journal for Numerical Methods in Engineering, 70(6), 705-727. doi:10.1002/nme.1903
Díez, P., José Ródenas, J., & Zienkiewicz, O. C. (2007). Equilibrated patch recovery error estimates: simple and accurate upper bounds of the error. International Journal for Numerical Methods in Engineering, 69(10), 2075-2098. doi:10.1002/nme.1837
Ródenas, J. J., González-Estrada, O. A., Díez, P., & Fuenmayor, F. J. (2010). Accurate recovery-based upper error bounds for the extended finite element framework. Computer Methods in Applied Mechanics and Engineering, 199(37-40), 2607-2621. doi:10.1016/j.cma.2010.04.010
Ainsworth, M., & Oden, J. T. (2000). A Posteriori Error Estimation in Finite Element Analysis. doi:10.1002/9781118032824
Xiao, Q. Z., & Karihaloo, B. L. (2006). Improving the accuracy of XFEM crack tip fields using higher order quadrature and statically admissible stress recovery. International Journal for Numerical Methods in Engineering, 66(9), 1378-1410. doi:10.1002/nme.1601
Bordas, S., & Duflot, M. (2007). Derivative recovery and a posteriori error estimate for extended finite elements. Computer Methods in Applied Mechanics and Engineering, 196(35-36), 3381-3399. doi:10.1016/j.cma.2007.03.011
Bordas, S., Duflot, M., & Le, P. (2007). A simple error estimator for extended finite elements. Communications in Numerical Methods in Engineering, 24(11), 961-971. doi:10.1002/cnm.1001
Duflot, M., & Bordas, S. (2008). A posteriorierror estimation for extended finite elements by an extended global recovery. International Journal for Numerical Methods in Engineering, 76(8), 1123-1138. doi:10.1002/nme.2332
Ródenas, J. J., González-Estrada, O. A., Tarancón, J. E., & Fuenmayor, F. J. (2008). A recovery-type error estimator for the extended finite element method based onsingular+smoothstress field splitting. International Journal for Numerical Methods in Engineering, 76(4), 545-571. doi:10.1002/nme.2313
Abel, J. F., & Shephard, M. S. (1979). An algorithm for multipoint constraints in finite element analysis. International Journal for Numerical Methods in Engineering, 14(3), 464-467. doi:10.1002/nme.1620140312
Farhat, C., Lacour, C., & Rixen, D. (1998). Incorporation of linear multipoint constraints in substructure based iterative solvers. Part 1: a numerically scalable algorithm. International Journal for Numerical Methods in Engineering, 43(6), 997-1016. doi:10.1002/(sici)1097-0207(19981130)43:6<997::aid-nme455>3.0.co;2-b
Van Loon, R., Anderson, P. D., de Hart, J., & Baaijens, F. P. T. (2004). A combined fictitious domain/adaptive meshing method for fluid–structure interaction in heart valves. International Journal for Numerical Methods in Fluids, 46(5), 533-544. doi:10.1002/fld.775
Guo, B., & Babuška, I. (1986). The h-p version of the finite element method. Computational Mechanics, 1(1), 21-41. doi:10.1007/bf00298636
Ródenas, J. J., Bugeda, G., Albelda, J., & Oñate, E. (2011). On the need for the use of error-controlled finite element analyses in structural shape optimization processes. International Journal for Numerical Methods in Engineering, 87(11), 1105-1126. doi:10.1002/nme.3155
FUENMAYOR, F. J., & OLIVER, J. L. (1996). CRITERIA TO ACHIEVE NEARLY OPTIMAL MESHES IN THEh-ADAPTIVE FINITE ELEMENT METHOD. International Journal for Numerical Methods in Engineering, 39(23), 4039-4061. doi:10.1002/(sici)1097-0207(19961215)39:23<4039::aid-nme37>3.0.co;2-c
Zienkiewicz, O. C., & Zhu, J. Z. (1992). The superconvergent patch recovery anda posteriori error estimates. Part 2: Error estimates and adaptivity. International Journal for Numerical Methods in Engineering, 33(7), 1365-1382. doi:10.1002/nme.1620330703
Zienkiewicz, O. C., Zhu, J. Z., & Wu, J. (1993). Superconvergent patch recovery techniques - some further tests. Communications in Numerical Methods in Engineering, 9(3), 251-258. doi:10.1002/cnm.1640090309
Zienkiewicz, O. C., & Zhu, J. Z. (1995). Superconvergence and the superconvergent patch recovery. Finite Elements in Analysis and Design, 19(1-2), 11-23. doi:10.1016/0168-874x(94)00054-j
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