[1] |
Adjerid, S., Aiffa, M., and Flaherty, J. 1998. Computational methods for singularly perturbed systems. InSingular Perturbation Concepts of Differential Equations, J. Cronin and R. O’Malley (Eds), AMS, Providence, RI. |
[2] |
Ainsworth, M. and Oden, J. T. 2000.a posteriori Error Estimation in Finite Element Analysis. Wiley, New York. · Zbl 1008.65076 |
[3] |
Ainsworth, M. and Senior, B. 1997. An adaptive refinement strategy for h-p finite element computations.Appl. Numer. Math. 26, 1–2, 165–178. · Zbl 0906.73057 |
[4] |
Ainsworth, M. and Senior, B. 1999.hp-finite element procedures on non-uniform geometric meshes: Adaptivity and constrained approximation. InGrid Generation and Adaptive Algorithms, M. W. Bern, J. E. Flaherty, and M. Luskin, (Eds.), IMA Volumes in Mathematics and its Applications, Vol. 113, Springer-Verlag, Berlin, 1–28. |
[5] |
Andreani, R., Birgin, E. G., Martinez, J. M., and Schuverdt, M. L. 2007. On augmented Lagrangian methods with general lower-level constraints.SIAM J. Optim. 18, 1286–1309. · Zbl 1151.49027 · doi:10.1137/060654797 |
[6] |
Babuška, I. and Suri, M. 1987. Theh-pversion of the finite element method with quasiuniform meshes.RAIRO Modél. Math. Anal. Numér. 21, 199–238. |
[7] |
Babuška, I. and Suri, M. 1990. Thep- andh-pversions of the finite element method, an overview.Comput. Methods Appl. Mech. Engrg. 80, 5–26. |
[8] |
Bank, R. E. and Nguyen, H. 2011.hpadaptive finite elements based on derivative recovery and superconvergence.Comput. Visual. Sci. 14, 287–299. · Zbl 1380.65358 |
[9] |
Bey, K. S. 1994. Anhpadaptive discontinuous Galerkin method for hyperbolic conservation laws. Ph.D. thesis, University of Texas at Austin, Austin, TX. |
[10] |
Birgin, E. G. 2005. TANGO home page. http://www.ime.usp.br/ egbirgin/tango/. |
[11] |
Bürg, M. and Dörfler, W. 2011. Convergence of an adaptivehpfinite element strategy in higher space-dimensions.Appl. Numer. Math. 61, 1132–1146. |
[12] |
Demkowicz, L. 2007.Computing with hp-adaptive Finite Elements, Vol 1, One and Two Dimensional Elliptic and Maxwell Problems. Chapman & Hall/CRC, Boca Raton, FL. · Zbl 1111.65103 |
[13] |
Demkowicz, L., Rachowicz, W., and Devloo, P. 2002. A fully automatic hp-adaptivity.J. Sci. Comput. 17, 127–155. · Zbl 0999.65121 · doi:10.1023/A:1015192312705 |
[14] |
Eibner, T. and Melenk, J. M. 2007. An adaptive strategy forhp-FEM based on testing for analyticity.Comput. Mech. 39, 5, 575–595. · Zbl 1163.65331 · doi:10.1007/s00466-006-0107-0 |
[15] |
Gui, W. and Babuška, I. 1986. Theh,pandh-pversions of the finite element method in 1 dimension. Part 3: The adaptiveh-pversion.Numer. Math. 49, 659–683. |
[16] |
Guo, B. and Babuška, I. 1986. Theh-pversion of the finite element method. Part 1: The basic approximation results.Comput. Mech. 1, 21–41. |
[17] |
Houston, P., Senior, B., and Süli, E. 2003. Sobolev regularity estimation forhp-adaptive finite element methods. InNumerical Mathematics and Advanced Appplications, F. Brezzi, A. Buffa, S. Corsaro, and A. Murli, Eds., Springer-Verlag, Berlin, 619–644. |
[18] |
Mavriplis, C. 1994. Adaptive mesh strategies for the spectral element method.Comput. Methods Appl. Mech. Engrg. 116, 77–86. · Zbl 0826.76070 · doi:10.1016/S0045-7825(94)80010-3 |
[19] |
Melenk, J. M. and Wohlmuth, B. I. 2001. On residual-based a-posteriori error estimation inhp-FEM.Adv. Comput. Math. 15, 311–331. · Zbl 0991.65111 · doi:10.1023/A:1014268310921 |
[20] |
Mitchell, W. F. 1991. Adaptive refinement for arbitrary finite element spaces with hierarchical bases.J. Comput. Appl. Math. 36, 65–78. · Zbl 0733.65066 · doi:10.1016/0377-0427(91)90226-A |
[21] |
Mitchell, W. F. 2012. PHAML home page. http://math.nist.gov/phaml. |
[22] |
Mitchell, W. F. 2013. A collection of 2D elliptic problems for testing adaptive grid refinement algorithms.Appl. Math. Comput. 220, 350–364. · Zbl 1329.65293 · doi:10.1016/j.amc.2013.05.068 |
[23] |
Mitchell, W. F. and McClain, M. A. 2011a. A comparison ofhp-adaptive strategies for elliptic partial differential equations (long version). NISTIR 7824, National Institute of Standards and Technology. |
[24] |
Mitchell, W. F. and McClain, M. A. 2011b. A survey ofhp-adaptive strategies for elliptic partial differential equations. InRecent Advances in Computational and Applied Mathematics, T. E. Simos, Ed., Springer, 227–258. · Zbl 1216.65159 · doi:10.1007/978-90-481-9981-5_10 |
[25] |
Oden, J. T. and Patra, A. 1995. A parallel adaptive strategy forhpfinite element computations.Comput. Methods Appl. Mech. Engrg. 121, 449–470. · Zbl 0851.73067 · doi:10.1016/0045-7825(94)00705-R |
[26] |
Oden, J. T., Patra, A., and Feng, Y. 1992. Anhpadaptive strategy. InAdaptive Multilevel and Hierarchical Computational Strategies, A. K. Noor, Ed., vol. 157, ASME Publication, 23–46. |
[27] |
Patra, A. and Gupta, A. 2001. A systematic strategy for simultaneous adaptivehpfinite element mesh modification using nonlinear programming.Comput. Methods Appl. Mech. Engrg. 190, 3797–3818. · Zbl 0990.65133 · doi:10.1016/S0045-7825(00)00298-X |
[28] |
Rachowicz, W., Oden, J. T., and Demkowicz, L. 1989. Toward a universal h-p adaptive finite element strategy, Part 3. Design of h-p meshes.Comput. Methods Appl. Mech. Engrg. 77, 181–212. · Zbl 0723.73076 · doi:10.1016/0045-7825(89)90131-X |
[29] |
Schmidt, A. and Siebert, K. G. 2000. a posteriori estimators for theh−pversion of the finite element method in 1D.Appl. Numer. Math. 35, 43–66. · Zbl 0966.65060 · doi:10.1016/S0168-9274(99)00046-X |
[30] |
Šolín, P., Červený, J., and Doležel, I. 2008. Arbitrary-level hanging nodes and automatic adaptivity in thehp-FEM.Math. Comput. Simulation 77, 117–132. |
[31] |
Šolín, P., Segeth, K., and Doležel, I. 2004.Higher-Order Finite Element Methods. Chapman & Hall/CRC, New York. |
[32] |
Süli, E., Houston, P., and Schwab, C. 2000.hp-finite element methods for hyperbolic problems. InThe Mathematics of Finite Elements and Applications X. MAFELAP, J. Whiteman, Ed., Elsevier, 143–162. · Zbl 0959.65127 |
[33] |
Szabo, B. and Babuška, I. 1991.Finite Element Analysis. Wiley, New York. |
[34] |
Wihler, T. P. 2011. An hp-adaptive strategy based on continuous sobolev embeddings.J. Comput. Appl. Math. 235, 8, 2731–2739. · Zbl 1209.65080 · doi:10.1016/j.cam.2010.11.023 |