[1] Gdoutos, E.E., Fracture Mechanics Criteria and Applications, Vol. 10 of Engineering Applications of Fracture Mechanics, Kluwer Academic Publishers, Dordrecht, 1990.
[2] Szabó, B., Babuška, I., Finite element analysis, John Wiley & Sons, New York, 1991.
[3] Kondrat’ev, V.A. Boundary-value problems for elliptic equations in domains with conical or angular points, Transactions of the Moscow Mathematical Society, 16, 1967, 227-313.
[4] Mazya, V.G., Plamenevskij, B.A., Lp-estimates of solutions of elliptic boundary value problems in domains with edges, Transactions of the Moscow Mathematical Society, 1, 1980, 49-97.
[5] Grisvard, P., Boundary Value Problems in Non-Smooth Domains, Pitman, London, 1985.
[6] Dauge, M., Elliptic Boundary Value Problems on Corner Domains, Vol. 1341 of Lecture Notes in Mathematics, Springer-Verlag, Berlin, 1988.
[7] Ciarlet, P., The Finite element method for elliptic problems, North-Holland, Amsterdam, 1978.
[8] Rukavishnikov, V.A., On the differential properties of -generalized solution of Dirichlet problem, Doklady Akademii Nauk SSSR, 309, 1989, 1318-1320.
[9] Rukavishnikov, V.A., On the uniqueness of the -generalized solution of boundary value problems with noncoordinated degeneration of the initial data, Doklady Mathematics, 63(1), 2001, 68-70.
[10] Rukavishnikov, V.A., On the existence and uniqueness of an -generalized solution of a boundary value problem with uncoordinated degeneration of the input data, Doklady Mathematics, 90(2), 2014, 562-564.
[11] Rukavishnikov, V.A., Rukavishnikova, E.I., Existence and uniqueness of an -generalized solution of the Dirichlet problem for the Lamé system with a corner singularity, Differential Equations, 55(6), 2019, 832-840.
[12] Rukavishnikov, V.A., Rukavishnikova, E.I., On the Dirichlet problem with corner singularity, Mathematics, 8(11), 2020, 1870.
[13] Rukavishnikov, V.A., Rukavishnikova, E.I., Finite-element method for the 1st boundary-value problem with the coordinated degeneration of the initial data, Doklagy Akademii Nauk, 338(6), 1994, 731-733.
[14] Rukavishnikov, V.A., Rukavishnikova, H.I., The finite element method for a boundary value problem with strong singularity, Journal of Computational and Applied Mathematics, 234(9), 2010, 2870-2882.
[15] Rukavishnikov, V.A., Mosolapov A.O., New numerical method for solving time-harmonic Maxwell equations with strong singularity, Journal of Computational Physics, 231, 2012, 2438-2448.
[16] Rukavishnikov, V.A., Mosolapov, A.O., Weighted edge finite element method for Maxwell’s equations with strong singularity, Doklady Mathematics, 87(2), 2013, 156-159.
[17] Rukavishnikov, V.A., Rukavishnikov, A.V., Weighted finite element method for the Stokes problem with corner singularity, Journal of Computational and Applied Mathematics, 341, 2018, 144-156.
[18] Rukavishnikov, V.A., Mosolapov, A.O., Rukavishnikova, E.I., Weighted finite element method for elasticity problem with a crack, Computers & Structures, 243, 2021, 106400.
[19] Zeng, W., Liu, G.R., Smoothed finite element methods (S-FEM): an overview and recent developments, Archives of Computational Methods in Engineering, 25, 2018, 397-435.
[20] Moës, N., Dolbow, J., Belytschko, T., A finite element method for crack growth without remeshing, International Journal for Numerical Methods in Engineering, 46, 1999, 131-150.
[21] Nicaise, S., Renard, Y., Chahine, E., Optimal convergence analysis for the extended finite element method, International Journal for Numerical Methods in Engineering, 86, 2011, 528-548.
[22] Sukumar, N., Dolbow, J.E., Moës, N., Extended finite element method in computational fracture mechanics: a retrospective examination, International Journal of Fracture, 196, 2015, 189-206.
[23] Francis, A., Ortiz-Bernardin, A., Bordas, S.P.A., Natarajan, S., Linear smoothed polygonal and polyhedral finite elements, International Journal for Numerical Methods in Engineering, 109, 2017, 1263-1288.
[24] Chen, J., Zhou, X., Zhou, L., Berto, F., Simple and effective approach to modeling crack propagation in the framework of extended finite element method, Theoretical and Applied Fracture Mechanics, 106, 2020, 102452.
[25] Zhou, X., Chen, J., Berto, F., XFEM based node scheme for the frictional contact crack problem, Computers & Structures, 231, 2020, 106221.
[26] Zeng, W., Liu, G.R., Jiang, C., Dong, X.W., Chen, H.D., Bao, Y. et al., An effective fracture analysis method based on the virtual crack closure-integral technique implemented in CS-FEM, Applied Mathematical Modelling, 40(3), 2016, 3783-3800.
[27] Vu-Bac, N., Nguyen-Xuan, H., Chen, L., Bordas, S., Kerfriden, P, Simpson R.N., et al., A node-based smoothed eXtended finite element method (NS-XFEM) for fracture analysis, Computer Modeling in Engineering and Sciences, 73, 2011, 331-355.
[28] Bhowmick, S., Liu, G.R., On singular ES-FEM for fracture analysis of solids with singular stress fields of arbitrary order, Engineering Analysis with Boundary Elements, 86, 2018, 64-81.
[29] Chen, H., Wang, Q., Liu, G.R., Wang, Y., Sun, J., Simulation of thermoelastic crack problems using singular edge-based smoothed finite element method, International Journal of Mechanical Sciences, 115-116, 2016, 123-134.
[30] Nguyen-Xuan, H., Liu, G.R., Bordas, S., Natarajan, S., Rabczuk, T., An adaptive singular ES-FEM for mechanics problems with singular field of arbitrary order, Computer Methods in Applied Mechanics and Engineering, 253, 2013, 252-273.
[31] Zeng, W., Liu, G.R., Li, D., Dong, X.W., A smoothing technique based beta finite element method (b FEM) for crystal plasticity modeling, Computers & Structures, 162, 2016, 48-67.
[32] Surendran, M., Natarajan, S., Bordas, S.P.A., Palani, G.S., Linear smoothed extended finite element method, International Journal for Numerical Methods in Engineering, 112, 2017, 1733-1749.
[33] Belytschko, T., Gu, L., Lu, Y.Y., Fracture and crack growth by element free Galerkin methods, Modelling and Simulation in Materials Science and Engineering, 2, 1994, 519-534.
[34] Nguyen, N.T., Bui, T.Q., Zhang, C.Z., Truong, T.T., Crack growth modeling in elastic solids by the extended meshfree Galerkin radial point interpolation method, Engineering Analysis with Boundary Elements, 44, 2014, 87-97.
[35] Khosravifard, A., Hematiyan, M.R., Bui, T.Q., Do, T.V., Accurate and efficient analysis of stationary and propagating crack problems by meshless methods, Theoretical and Applied Fracture Mechanics, 87, 2017, 21-34.
[36] Racz, D., Bui, T.Q., Novel adaptive meshfree integration techniques in meshless methods, International Journal for Numerical Methods in Engineering, 90, 2012, 1414-1434.
[37] Aghahosseini, A., Khosravifard, A., Bui, T.Q., Efficient analysis of dynamic fracture mechanics in various media by a novel meshfree approach, Theoretical and Applied Fracture Mechanics, 99, 2019, 161-176.
[38] Ma, W., Liu, G., Ma, H., A smoothed enriched meshfree Galerkin method with twolevel nesting triangular sub-domains for stress intensity factors at crack tips, Theoretical and Applied Fracture Mechanics, 101, 2019, 279-293.
[39] Zhou X., Jia Z., Wang L., A field-enriched finite element method for brittle fracture in rocks subjected to mixed mode loading, Engineering Analysis with Boundary Elements, 129, 2021, 105-124.
[40] Zhou, X., Wang, L., A field-enriched finite element method for crack propagation in fiber-reinforced composite lamina without remeshing, Composite Structures, 270, 2021, 114074.
[41] Wang L., Zhou X., A field-enriched finite element method for simulating the failure process of rocks with different defects, Computers & Structures, 250, 2021, 106539.
[42] Grisvard, P., Singularités en elasticité, Archive for Rational Mechanics and Analysis, 107(3), 1989, 157–180.
[43] Rukavishnikov, V.A., The Dirichlet problem for a second-order elliptic equation with noncoordinated degeneration of the input data, Differential Equations, 32(3), 1996, 406-412.
[44] Rukavishnikov, V.A., Kuznetsova, E.V., Coercive estimate for a boundary value problem with noncoordinated degeneration of the data, Differential Equations, 43(4), 2007, 550-560.
[45] Rukavishnikov, V.A., Weighted FEM for two-dimensional elasticity problem with corner singularity, Lecture Notes in Computational Science and Engineering, 112, 2016, 411-419.