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[1] Aragón A.M., Duarte C.A., Geubelle P.H., Generalized finite element enrichment functions for discontinuous gradient fields, Internat. J. Numer. Methods Engrg., 2010, 82(2), 242–268 [2] Babuška I., Banerjee U., Stable generalized finite element method, Comput. Methods Appl. Mech. Engrg. (in press), DOI: 10.1016/j.cma.2011.09.012 [3] Babuška I., Banerjee U., Osborn J.E., Meshless and generalized finite element methods: a survey of some major results, In: Meshfree Methods for Partial Differential Equations, Bonn, 2001, Lect. Notes Comput. Sci. Eng., 26

). Three-dimensional induction logging problems, Part 2: A finite-difference solution, Geophysics 67(2): 484-491. Pardo, D., Demkowicz, L., Torres-Verd´ın, C. and Paszynski, M. (2006). Two-dimensional high-accuracy simulation of resistivity logging-while-drilling (LWD) measurements using a self-adaptive goal-oriented hp finite element method, SIAM Journal on Applied Mathematics 66(6): 2085-2106. Pardo, D., Demkowicz, L., Torres-Verd´ın, C. and Paszynski, M. (2007). A self-adaptive goal-oriented hp-finite element method with electromagnetic applications, Part II

References 1. Stomatološki fakultet. Stomatološki materijali knjiga 2: Beograd; 2012. 2. Ming-Lun Hsu, Chih-Ling Chang, Application of Finite Element Analysis in Dentistry, Finite Element Analysis, ed. David Moratal, 2010. 3. Geng J, Yan W, Xu W (Eds.). Application of the Finite Element Method in Implant Dentistry, ISBN: 978-3-540- 73763-6, Springer, 2008. 4. Duygu Koc, Arife Dogan, and Bulent Bek, Bite Force and Influential Factors on Bite Force Measurements: A Literature Review. Eur J Dent, 2010;4:223-232. 5. Olmsted MJ, Wall CE, Vinyard CJ. Human bite force

Journal of Applied Analysis Vol. 7, No. 2 (2001), pp. 257–269 GRADIENT-FINITE ELEMENT METHOD FOR NONLINEAR NEUMANN PROBLEMS I. FARAGÓ and J. KARÁTSON Received November 27, 2000 and, in revised form, March 20, 2001 Abstract. We consider the numerical solution of quasilinear elliptic Neumann problems. The basic difficulty is the non-injectivity of the operator, which can be overcome by suitable factorization. We extend the gradient-finite element method (GFEM), introduced earlier by the authors for Dirichlet problems, to the Neumann problem. The algorithm is

diffusion equation. To simplify the exposition, we consider only the case of polygonal/polyhedral domains and subdomains, and the case of homogeneous Neumann conditions. For the condensed matrix arising in mixed hybrid or mixed macro-hybrid finite element methods we describe the general idea for construction of preconditioners with special projectors [4] . In Section 2 , we consider the model diffusion problem in the square domain partitioned in square subdomains with constant diffusion and reaction coefficients in subdomains. Based on the results of Section 1 we

. Appl. Math. 62 (2002), 870–887. [16] C. Li, Z. Zhao, and Y. Chen, Numerical approximation and error estimates of a time fractional order diffusion equation. In: Proc. of the ASME 2009 Intern. Design Engineering Technical Conf. and Computers and Information in Engineering Conf. IDETC/CIE 2009, San Diego, California, USA. [17] Y. Jiang and J. Ma, High-order finite element methods for timefractional partial differential equations. J. Comput. Appl. Math. 235

1 Introduction The beginning of the analysis of the mixed finite element methods for solving problems of the theories of plates, thin and medium thickness shells dates back to the 60s of the preceding century. Among pioneering, papers [ 10 , 11 , 32 , 23 , 12 , 24 , 22 ] can be mentioned. The research in this area is still very intensive. See, for example, [ 28 ] and the articles cited therein. The presented work is devoted to the study of a mixed finite element method for geometrically nonlinear problems in the theory of thin elastic shells. The method of

, Physical Review E 92 : 053202. Karczewska, A., Szczeciński, M., Rozmej, P., and Boguniewicz, B. (2016). Finite element method for stochastic extended KdV equations, Computational Methods in Science and Technology 22 (1): 19–29. Kim, J.W., Bai, K.J., Ertekin, R.C. and Webster, W.C. (2001). A derivation of the Green–Naghdi equations for irrotational flows, Journal of Engineering Mathematics 40 : 17–42. Marchant, T. and Smyth, N. (1990). The extended Korteweg–de Vries equation and the resonant flow of a fluid over topography, Journal of Fluid Mechanics 221 (1): 263

boundary condition of the potential field changes from a pure Neumann condition on anodes and the insulated part to a nonlinear one on cathodes. This causes local solution singularities around the interface between different parts of the boundary [ 12 , 13 ]. Hence, the adaptive technique is a natural choice for its efficient numerical simulation. In this work, we develop and analyze an adaptive finite element method (AFEM) for the system ( 1.1 )–( 1.2 ). A typical adaptive algorithm comprises successive iterations of the following loop: (1.5) SOLVE → ESTIMATE → MARK

, International Journal for Numerical Methods in Engineering, 44 (9), 1267-1282, 1999. 5. J.C. Galvez, J. Cervenka, D.A. Cendon, V. Saouma, A discrete crack approach to normal/shearcracking of concrete, Cement and Concrete Research, 32 (10), 1567-1585, 2002. 6. F. Zhou, J.F. Molinari, Dynamic crack propagation with cohesive elements: a methodology to addressmesh dependency, International Journal for Numerical Methods in Engineering, 59 (1), 1-24, 2004. 7. T. Belytschko, J. Fish, B.E. Englemann, A finite element method with embedded localization zones, Computer Methods in