Диссертация (1149340), страница 23
Текст из файла (страница 23)
Z. A simple error estimator and adaptive procedure for practicalengineering analysis // Internat. J. Numer. Meth. Engrg. 1987. Т. 24, № 2. С. 337–357.73. Eriksson K., C.Johnson. An adaptive finite element method for linear elliptic problems //Math. Comp. 1988. Т. 50, № 182. С. 361–383.74. Johnson C., Hansbo P. Adaptive finite elements in computational mechanics // Comput.Methods Appl. Mech. Engrg. 1992. Т. 101, № 1-2. С.
143–181.75. Ainsworth M., Oden J. T. A procedure for a posteriori error estimation for h-p finite elementmethods // Comput. Methods Appl. Mech. Engrg. 1992. Т. 101, № 1-3. С. 73–96.76. Ainsworth M., Oden J. T. A unified approach to a posteriori error estimation using elementresidual methods // Numer. Math. 1993. Т. 65, № 1. С. 23–50.77. Verfürth R. A review of a posteriori error estimation and adaptive mesh-refinementtechniques. Wiley and Sons, Teubner, New-York, 1996.78.
Dörfler W., Rumpf M. An adaptive strategy for elliptic problems including a posterioricontrolled boundary approximation // Math. Comp. 1998. Т. 67, № 224. С. 1361–1382.13379. Carstensen C. Quasi–interpolation and a posteriori error analysis of finite element methods //Mathematical Modelling in Numerical Analysis. 1999. Т. 6, № 33. С. 1187–1202.80.
Carstensen C., Verfürth R. Edge residuals dominate a posteriori error estimates for low orderfinite element methods // SIAM J. Numer. Anal. 1999. Т. 5, № 36. С. 1571–1587.81. Ainsworth M., Oden J. T. A posteriori error estimation in finite element analysis. Wiley andSons, New York, 2000.82. Carstensen C., Funken S. A. Fully reliable localized error control in the FEM // SIAM J.Sci. Comput. 2000.
Т. 21, № 4. С. 1465–1484.83. Babuška I., Strouboulis T. The finite element method and its reliability. New York: TheClarendon Press Oxford University Press, 2001. С. xii+802.84. Babuška I., Whiteman J. R., Strouboulis T. Finite elements, an introduction to the methodand error estimation. Oxford University Press, New York, 2011.85. Zienkiewicz O.
C., Zhu J. Z. Adaptive techniques in the finite element method // Commun.Appl. Numer. Methods. 1988. Т. 4. С. 197–204.86. Babuška I. M., Rodrı́guez R. The problem of the selection of an a posteriori error indicatorbased on smoothening techniques // Internat. J. Numer. Methods Engrg. 1993. Т. 36, № 4.С. 539–567.87. Zienkiewicz O. C., Boroomand B., Zhu J. Z. Recovery procedures in error estimation andadaptivity: adaptivity in linear problems // Advances in adaptive computational methods inmechanics (Cachan, 1997) / под ред. P.
Ladeveze, J.T. Oden. Amsterdam: Elsevier, 1998.Т. 47. С. 3–23.88. Wang J. Superconvergence analysis of finite element solutions by the least-squares surfacefitting on irregular meshes for smooth problems // J. Math. Study. 2000. Т. 33. С. 229–243.89. Bartels S., Carstensen C. Each averaging technique yields reliable a posteriori error controlin FEM on unstructured grids. Part II: Higher order FEM // Math. Comput. 2002. Т. 239,№ 71. С.
971–994.90. Wang J., Ye X. Superconvergence analysis for the Navier–Stokes equations // AppliedNumerical Mathematics. 2002. Т. 41. С. 515–527.91. Heimsund B.-O., Tai X.-C., Wang J. Superconvergence for the gradient of finite elementapproximations by L2 projections // SIAM J. Numer. Anal. 2002. Т. 40, № 4. С. 1263–1280.92. Zhang Zh., Naga A. A new finite element gradient recovery method: superconvergenceproperty // SIAM J. Sci. Comput. 2005.
Т. 26, № 4. С. 1192–1213.13493. Oganesjan L. A., Ruhovec L. A. An investigation of the rate of convergence of variationdifference schemes for second order elliptic equations in a two-dimensional region with smoothboundary // Ž. Vyčisl. Mat. i Mat. Fiz. 1969. Т. 9. С. 1102–1120.94. Zlámal M. Some superconvergence results in the finite element method // Mathematicalaspects of finite element methods (Proc. Conf., Consiglio Naz. delle Ricerche (C.N.R.), Rome,1975). Springer, Berlin, 1977.
С. 353–362. Lecture Notes in Math., Vol. 606.95. Křı́žek M., Neittaanmäki P. Superconvergence phenomenon in the finite element methodarising from averaging gradients // Numer. Math. 1984. Т. 45, № 1. С. 105–116.96. Křı́žek M., Neittaanmäki P. On superconvergence techniques // Acta Appl. Math. 1987.Т. 9, № 3. С. 175–198.97. Křížek M., Neittaanmäki P., Stenberg R. Superconvergence, post-processing and a posteriorierror estimates // Lecture notes in pure and applied mathematics / под ред. M.
Křížek,P. Neittaanmäki, R. Stenberg. Marcel Dekker, New York, 1998. Т. 196.98. Wahlbin L. B. Superconvergence in Galerkin finite element methods. Berlin: Springer-Verlag,1995. Т. 1605. С. xii+166.99. Ladevéze P., Leguillon D. Error estimate procedure in the finite element method andapplications // SIAM J. Numer.
Anal. 1983. Т. 20, № 3. С. 485–509.100. Ainsworth M. A posteriori error estimation for fully discrete hierarchic models of ellipticboundar–value problems on thin domains // Numer. Math. 1998. Т. 80, № 3. С. 325–362.101. Ainsworth M., Rankin R. Fully computable error bounds for discontinuous Galerkin FiniteElement Approximations on Meshes with an Arbitrary Number of Levels of Hanging Nodes //SIAM J.
Numer. Anal. 2010. Т. 47, № 6. С. 4112–4141.102. Deuflhard P., Leinen P., Yserentant H. Concept of an adaptive hierarchical finite elementcode // Impact Computing Sci. Engrg. 1989. Т. 1, № 1. С. 3–35.103. Agouzal A. On the saturation assumption and hierarchical a posteriori error estimator //Comput. Meth. Appl. Math. 2002. Т. 2, № 2. С. 125–131.104. Duran R., Muschietti M. A., Rodriguez R.
On the asymptotic exactness of error estimatorsfor linear triangle elements // Numer. Math. 1991. Т. 59, № 2. С. 107–127.105. Dörfler W., Nochetto R. H. Small data oscillation implies the saturation assumption //Numer. Math. 2002. Т. 91, № 1. С. 1–12.106. Becker R., Rannacher R. A feed–back approach to error control in finite element methods:Basic approach and examples // East–West J.
Numer. Math. 1996. Т. 4, № 4. С. 237–264.135107. Stein E., Ohnimus S. Coupled model- and solution-adaptivity in the finite element method //Comput. Methods Appl. Mech. Engrg. 1997. Т. 150, № 1–4. С. 327–350.108. Peraire J., Patera A. T. Bounds for linear-functional outputs of coercive partial differentialequations: Local indicators and adaptive refinement // Advances in adaptive computationalmethods in mechanics / под ред. P. Ladevéze, J.
T. Oden. Elsevier, New York, 1998. С. 199–228.109. Houston P., Rannacher R., Süli E. A posteriori error analysis for stabilised finite elementapproximations of transport problems // Comput. Methods Appl. Mech. Engrg. 2000. Т.190, № 11–12. С. 1483–1508.110. Rannacher R. The dual-weighted-residual method for error control and mesh adaptationin finite element methods // The mathematics of finite elements and applications, X,MAFELAP 1999 (Uxbridge). Oxford: Elsevier, 2000.
С. 97–116.111. Oden J. T., Prudhomme S. Goal–oriented error estimation and adaptivity for the finiteelement method // Comput. Methods Appl. 2001. Т. 41, № 5–6. С. 735–756.112. Stein E., Rüter M., Ohnimus S. Error-controlled adaptive goal-oriented modeling and finiteelement approximations in elasticity // Comput. Methods Appl. Mech. Engrg.
2007. Т. 196,№ 37–40. С. 3598–3613.113. Meidner D., Rannacher R., Vihharev J. Goal-oriented error control of the iterative solutionof finite element equations // J. Numer. Math. 2009. Т. 17, № 2. С. 143–172.114. Rannacher R., Vexler B. Adaptive finite element discretization in PDE-based optimization //GAMM-Mitt. 2010. Т. 33, № 2. С. 177–193.115. Besier M., Rannacher R. Goal-oriented space-time adaptivity in the finite element Galerkinmethod for the computation of nonstationary incompressible flow // Internat. J. Numer.Methods Fluids. 2012.
Т. 70, № 9. С. 1139–1166.116. Prager W., Synge J. L. Approximation in elasticity based on the concept of function space //Quart. Appl. Math. 1947. № 5. С. 241–269.117. Synge J. L. The method of the hypercircle in function-space for boundary-value problems //Proc. Roy. Soc. London. Ser. A. 1947. Т. 191. С. 447–467.118. Mikhlin S.
G. Variational methods in mathematical physics. Pergamon, Oxford, 1964.119. Repin S. I., Xanthis L. S. A posteriori error estimation for elastoplastic problems based onduality theory // Comput. Methods Appl. Mech. Engrg. 1996. Т. 138, № 1-4. С. 317–339.120. Repin S. A posteriori estimates for approximate solutions of variational problems withstrongly convex functionals // Problems of Mathematical Analysis.
1997. Т. 17. С. 199–226.136121. Repin S. A posteriori error estimation for variational problems with power growth functionalsbased on duality theory // Zapiski Nauchnych Seminarov POMI. 1997. Т. 249. С. 244–255.122. Repin S. I. A unified approach to a posteriori error estimation based on duality errormajorants // Math. Comput.
Simulation. 1999. Т. 50, № 1-4. С. 305–321.123. Repin S. A posteriori error estimation for variational problems with uniformly convexfunctionals // Math. Comput. 2000. Т. 69, № 230. С. 481–500.124. Raviart P.-A., Thomas J. M. A mixed finite element method for 2nd order elliptic problems //Mathematical aspects of finite element methods (Proc.
Conf., Consiglio Naz. delle Ricerche(C.N.R.), Rome, 1975). Springer, Berlin, 1977. С. 292–315. Lecture Notes in Math., Vol.606.125. Nédélec J.-C. A new family of mixed finite elements in R3 // Numer. Math. 1986. Т. 50,№ 1. С. 57–81.126. Efficient rectangular mixed finite elements in two and three space variables / F. Brezzi,J. Douglas, Jr., M. Fortin [и др.] // RAIRO Modél. Math. Anal. Numér. 1987.
Т. 21, № 4.С. 581–604.127. Mixed finite elements for second order elliptic problems in three variables / F. Brezzi,J. Douglas, Jr., R. Durán [и др.] // Numer. Math. 1987. Т. 51, № 2. С. 237–250.128. Mali O., Neittaanmäki P., Repin S. Accuracy verification methods. Springer, Dordrecht,2014. Т.
![](https://s.studizba.com/z.php?f=/templates/si/i/noavatar.png&w=100&h=100&t=1"){kind=avatar}
