المؤلفون: Lin, Qun, Xie, Hehu

مصطلحات موضوعية: keyword:multilevel correction, keyword:adaptive finite element method, keyword:Steklov eigenvalue problem, keyword:numerical experiment, msc:35P15, msc:65N25, msc:65N30

وصف الملف: application/pdf

Relation: mr:MR3204407; zbl:Zbl 1313.65298

الاتاحة: http://hdl.handle.net/10338.dmlcz/702900

المؤلفون: Dai, Xiaoying, He, Lianhua, Zhou, Aihui

مصطلحات موضوعية: keyword:adaptive finite element method, keyword:elliptic partial differential equations, keyword:perturbation argument, keyword:boundary value problem, keyword:eigenvalue problem, keyword:convergence, keyword:nonlinear boundary value problem, keyword:nonlinear eigenvalue problem, msc:35J25, msc:35J60, msc:35P15, msc:35P30, msc:65N12, msc:65N25, msc:65N30

وصف الملف: application/pdf

Relation: mr:MR3204453; zbl:Zbl 1313.65300

الاتاحة: http://hdl.handle.net/10338.dmlcz/702893

المؤلفون: Lin, Qun, Xie, Hehu, Xu, Fei

مصطلحات موضوعية: keyword:semilinear elliptic problem, keyword:multilevel correction, keyword:adaptive finite element method, msc:35J61, msc:62F35, msc:65B99, msc:65N30

وصف الملف: application/pdf

Relation: mr:MR3396479; zbl:Zbl 06486924; reference:[1] Adams, R. A.: Sobolev Spaces.Pure and Applied Mathematics 65. A Series of Monographs and Textbooks Academic Press, New York (1975). Zbl 0314.46030, MR 0450957; reference:[2] Babuška, I., Miller, A.: A feedback finite element method with a posteriori error estimation. I. The finite element method and some basic properties of the a posteriori error estimator.Comput. Methods Appl. Mech. Eng. 61 (1987), 1-40. Zbl 0593.65064, MR 0880421, 10.1016/0045-7825(87)90114-9; reference:[3] Babuška, I., Rheinboldt, W. C.: Error estimates for adaptive finite element computations.SIAM J. Numer. Anal. 15 (1978), 736-754. Zbl 0398.65069, MR 0483395, 10.1137/0715049; reference:[4] Babuška, I., Strouboulis, T.: The Finite Element Method and Its Reliability.Numerical Mathematics and Scientific Computation Clarendon Press, Oxford (2001). MR 1857191; reference:[5] Babuška, I., Vogelius, M.: Feedback and adaptive finite element solution of one-dimensional boundary value problems.Numer. Math. 44 (1984), 75-102. Zbl 0574.65098, MR 0745088, 10.1007/BF01389757; reference:[6] Brenner, S. C., Scott, L. R.: The Mathematical Theory of Finite Element Methods.Texts in Applied Mathematics 15 Springer, New York (1994). Zbl 0804.65101, MR 1278258, 10.1007/978-1-4757-4338-8_7; reference:[7] Cascon, J. M., Kreuzer, C., Nochetto, R. H., Siebert, K. G.: Quasi-optimal convergence rate for an adaptive finite element method.SIAM J. Numer. Anal. 46 (2008), 2524-2550. Zbl 1176.65122, MR 2421046, 10.1137/07069047X; reference:[8] Ciarlet, P. G.: The Finite Element Method for Elliptic Problems.Studies in Mathematics and Its Applications. Vol. 4 North-Holland Publishing Company, Amsterdam (1978). Zbl 0383.65058, MR 0520174; reference:[9] Dörfler, W.: A convergent adaptive algorithm for Poisson's equation.SIAM J. Numer. Anal. 33 (1996), 1106-1124. Zbl 0854.65090, MR 1393904, 10.1137/0733054; reference:[10] He, L., Zhou, A.: Convergence and optimal complexity of adaptive finite element methods for elliptic partial differential equations.Int. J. Numer. Anal. Model. 8 (2011), 615-640. MR 2805661; reference:[11] Holst, M., McCammom, J. A., Yu, Z., Zhou, Y., Zhu, Y.: Adaptive finite element modeling techniques for the Possion-Boltzmann equation.Commun. Comput. Phys. 11 (2012), 179-214. MR 2841952, 10.4208/cicp.081009.130611a; reference:[12] Lin, Q., Xie, H.: A multilevel correction type of adaptive finite element method for Steklov eigenvalue problems.Proc. Internat. Conference `Applications of Mathematics', Prague, 2012. In Honor of the 60th Birthday of M. Křížek Academy of Sciences of the Czech Republic, Institute of Mathematics, Prague (2012), 134-143 J. Brandts et al. Zbl 1313.65298, MR 3204407; reference:[13] Lin, Q., Xie, H.: A multi-level correction scheme for eigenvalue problems.Math. Comput. 84 (2015), 71-88. Zbl 1307.65159, MR 3266953, 10.1090/S0025-5718-2014-02825-1; reference:[14] Mekchay, K., Nochetto, R. H.: Convergence of adaptive finite element methods for general second order linear elliptic PDEs.SIAM J. Numer. Anal. 43 (2005), 1803-1827. Zbl 1104.65103, MR 2192319, 10.1137/04060929X; reference:[15] Morin, P., Nochetto, R. H., Siebert, K. G.: Data oscillation and convergence of adaptive FEM.SIAM J. Numer. Anal. 38 (2000), 466-488. Zbl 0970.65113, MR 1770058, 10.1137/S0036142999360044; reference:[16] Morin, P., Nochetto, R. H., Siebert, K. G.: Convergence of adaptive finite element methods.SIAM Rev. 44 (2002), 631-658. Zbl 1016.65074, MR 1980447, 10.1137/S0036144502409093; reference:[17] Stevenson, R.: Optimality of a standard adaptive finite element method.Found. Comput. Math. 7 (2007), 245-269. Zbl 1136.65109, MR 2324418, 10.1007/s10208-005-0183-0; reference:[18] Stevenson, R.: The completion of locally refined simplicial partitions created by bisection.Math. Comput. 77 (2008), 227-241. Zbl 1131.65095, MR 2353951, 10.1090/S0025-5718-07-01959-X; reference:[19] Xie, H.: A multilevel correction type of adaptive finite element method for eigenvalue problems.ArXiv:1201.2308 (2012). MR 3204407

الاتاحة: http://hdl.handle.net/10338.dmlcz/144390