Publications of Douglas N. Arnold

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Talk slidesStudent thesesIMA “From the Director” columns

  Douglas N. Arnold and Jeonghun J. Lee. Mixed methods for elastodynamics with weak symmetry. To appear in SIAM. J. Numer. Anal. arXiv preprint 1312.6319, 2013. [ bib | pdf | Abstract ]
  Douglas N. Arnold, Gerard Awanou, and Weifeng Qiu. Mixed finite elements for elasticity on quadrilateral meshes. Adv. Comput. Math., 2014. Published online September 9, 2014. arXiv preprint 1306.6821. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Daniele Boffi, and Francesca Bonizzoni. Finite element differential forms on curvilinear cubic meshes and their approximation properties. Numer. Math., 2014. Published online April 30, 2014. arXiv preprint 1204.2595. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Gerard Awanou. Finite element differential forms on cubical meshes. Math. Comput., 83:1551-1570, 2014. Published online October 17, 2013. arXiv preprint 1204.2595. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Richard S. Falk, Johnny Guzmán, and Gantumur Tsogtgerel. On the consistency of the combinatorial codifferential. Trans. Amer. Math. Soc., 2014. Posted on February 26, 2014, to appear in print. arXiv preprint 1204.2595. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Gerard Awanou, and Ragnar Winther. Nonconforming tetrahedral mixed finite elements for elasticity. Math. Models Methods Appl. Sci., 24:783-796, 2014. Published online 1 August 2013. arXiv preprint 1210.6256. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold. The flight of a golf ball. In Nicholas J. Higham, editor, The Princeton Companion to Applied Mathematics. Princeton University Press, Princeton, NJ, 2012. To appear. [ bib | pdf | Abstract ]
  Douglas N. Arnold. Stability, consistency, and convergence of numerical discretizations. In Björn Engquist, editor, Encyclopedia of Applied and Computational Mathematics. Springer, 2012. To appear. [ bib | pdf | Abstract ]
  Douglas N. Arnold and Hongtao Chen. Finite element exterior calculus for parabolic problems. In revision. arXiv preprint 1209.1142, 2012. [ bib | pdf | Abstract ]
  Douglas N. Arnold. Spaces of finite element differential forms. In U. Gianazza, F. Brezzi, P. Colli Franzone, and G. Gilardi, editors, Analysis and Numerics of Partial Differential Equations, pages 117-140. Springer, 2013. arXiv preprint 1208.2041. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Henry Cohn. Mathematicians take a stand. Notices Amer. Math. Soc., 59(6):828-833, 2012. arXiv preprint 1204.1351. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Richard S. Falk, and Jay Gopalakrishnan. Mixed finite element approximation of the vector Laplacian with Dirichlet boundary conditions. Math. Models Methods Appl. Sci., 22(9):26 pages, 2012. arXiv preprint 1109.3668. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold. Challenges and responses in mathematical research publishing. In Tony Mayer and Nicholas Steneck, editors, Promoting Research Integrity in a Global Environment, pages 301-304. World Scientific, Singapore, 2012. [ bib | pdf | Abstract ]
  Douglas N. Arnold and Kristine K. Fowler. Nefarious Numbers. Notices Amer. Math. Soc., 58(3):434-437, 2011. Also appeared in Gazette of the Australian Mathematical Society 38(1):9-16, 2011; Newsletter of the European Mathematical Society 80:34-36, 2011; and, in Russian translation, in a volume on bibliometrics, Moscow, 2011. [ bib | pdf | Abstract ]
  Douglas N. Arnold and Gerard Awanou. The serendipity family of finite elements. Found. Comput. Math., 11:337-344, 2011. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold. The science of a drive. Notices Amer. Math. Soc., 57(4):498-501, 2010. Also appeared in the collection Mathematics and Sports, J. Gallian, ed., Mathematical Association of America Dolciani Mathematical Expositions # 43, 2010, 149-156. [ bib | pdf | Abstract ]
  Douglas N. Arnold, Richard S. Falk, and Ragnar Winther. Finite element exterior calculus: from Hodge theory to numerical stability. Bull. Amer. Math. Soc. (N.S.), 47:281-354, 2010. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold. Integrity under attack: the state of scholarly publishing. SIAM News, 42(10):2-3, 2009. Spanish translation in Gac. R. Soc. Mat. Esp., 13(1):21-25, 2010; Chinese translation in Mathematical Culture 4, 2010. [ bib | pdf | Abstract ]
  Douglas N. Arnold and Marie Rognes. Stability of Lagrange elements for the mixed Laplacian. Calcolo, 46:245-260, 2009. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Richard S. Falk, and Ragnar Winther. Geometric decompositions and local bases for spaces of finite element differential forms. Comput. Methods Appl. Mech. Engrg., 198:1660-1672, 2009. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Jonathan Rogness. Möbius transformations revealed. Notices Amer. Math. Soc., 55:1226-1231, 2008. Chinese translation in Shu Xue Yi Lin, 28(2):109-115, 2009. [ bib | pdf | Abstract ]
  Douglas N. Arnold. Is the public hungry for math? Notices Amer. Math. Soc., 55:1069, 2008. Chinese translation in Shu Xue Yi Lin, 28(2):171-173, 2009. [ bib | pdf | Abstract ]
  Douglas N. Arnold, Gerard Awanou, and Ragnar Winther. Finite elements for symmetric tensors in three dimensions. Math. Comput., 77:1229-1251, 2008. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Richard S. Falk, and Ragnar Winther. Finite element differential forms. Proc. Appl. Math. Mech., 7:1021901-1021902, 2007. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Richard S. Falk, and Ragnar Winther. Mixed finite element methods for linear elasticity with weakly imposed symmetry. Math. Comput., 76:1699-1723, 2007. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Nicolae Tarfulea. Boundary conditions for the Einstein-Christoffel formulation of Einstein's equations. Electron. J. Differential Equations, Conf. 15:11-27, 2007. [ bib | pdf | Abstract ]
  Douglas N. Arnold, Franco Brezzi, Richard S. Falk, and Donatella Marini. Locking-free Reissner-Mindlin elements without reduced integration. Comput. Methods Appl. Mech. Engrg., 96:3660-3671, 2007. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Richard S. Falk, and Ragnar Winther. Finite element exterior calculus, homological techniques, and applications. Acta Numer., 15:1-155, 2006. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Richard S. Falk, and Ragnar Winther. Differential complexes and stability of finite element methods II: The elasticity complex. In D. Arnold, P. Bochev, R. Lehoucq, R. Nicolaides, and M. Shashkov, editors, Compatible Spatial Discretizations, volume 142 of IMA Vol. Math. Appl., pages 47-68. Springer, Berlin, 2006. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Richard S. Falk, and Ragnar Winther. Differential complexes and stability of finite element methods I: The de Rham complex. In D. Arnold, P. Bochev, R. Lehoucq, R. Nicolaides, and M. Shashkov, editors, Compatible Spatial Discretizations, volume 142 of The IMA Volumes in Mathematics and its Applications, pages 23-46. Springer, Berlin, 2006. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Gerard Awanou. Rectangular mixed finite elements for elasticity. Math. Models Methods Appl. Sci., 15(9):1417-1429, 2005. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Franco Brezzi, and L. Donatella Marini. A family of discontinuous Galerkin finite elements for the Reissner-Mindlin plate. J. Sci. Comput., 22/23:25-45, 2005. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Daniele Boffi, and Richard S. Falk. Quadrilateral H(div) finite elements. SIAM J. Numer. Anal., 42(6):2429-2451, 2005. [ bib | DOI | pdf | Abstract ]
  Alexander M. Alekseenko and Douglas N. Arnold. New first-order formulation for the Einstein equations. Phys. Rev. D (3), 68(6):064013, 6, 2003. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Alexandre L. Madureira. Asymptotic estimates of hierarchical modeling. Math. Models Methods Appl. Sci., 13(9):1325-1350, 2003. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Ragnar Winther. Mixed finite elements for elasticity in the stress-displacement formulation. In Z. Chen, R. Glowinski, and K. Li, editors, Current trends in scientific computing (Xi'an, 2002), volume 329 of Contemp. Math., pages 33-42. Amer. Math. Soc., Providence, RI, 2003. [ bib | pdf | Abstract ]
  Douglas N. Arnold and Ragnar Winther. Nonconforming mixed elements for elasticity. Math. Models Methods Appl. Sci., 13(3):295-307, 2003. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold. Differential complexes and numerical stability. In L. Tatsien, editor, Proceedings of the International Congress of Mathematicians, Vol. I (Beijing, 2002), pages 137-157, Beijing, 2002. Higher Ed. Press. Spanish translation in Gac. R. Soc. Mat. Esp., 8(2):335-360, 2005. [ bib | pdf | Abstract ]
  Douglas N. Arnold, Daniele Boffi, and Richard S. Falk. Remarks on quadrilateral Reissner-Mindlin plate elements. In H. Mang, F. Rammerstorfer, and J. Eberhardsteiner, editors, WCCM V - Fifth World Congress on Computational Mechanics, pages 137-157. Technical University of Vienna, 2002. [ bib | pdf | Abstract ]
  Douglas N. Arnold, Alexandre L. Madureira, and Sheng Zhang. On the range of applicability of the Reissner-Mindlin and Kirchhoff-Love plate bending models. J. Elasticity, 67(3):171-185 (2003), 2002. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Franco Brezzi, Bernardo Cockburn, and L. Donatella Marini. Unified analysis of discontinuous Galerkin methods for elliptic problems. SIAM J. Numer. Anal., 39(5):1749-1779, 2002. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Ragnar Winther. Mixed finite elements for elasticity. Numer. Math., 92(3):401-419, 2002. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Daniele Boffi, and Richard S. Falk. Approximation by quadrilateral finite elements. Math. Comp., 71(239):909-922, 2002. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Daniele Boffi, Richard S. Falk, and Lucia Gastaldi. Finite element approximation on quadrilateral meshes. Comm. Numer. Methods Engrg., 17(11):805-812, 2001. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold. Numerical problems in general relativity. In P. Neittaanmki, T. Tiihonen, and P. Tarvainen, editors, Numerical Mathematics and Advanced Applications. World Scientific, 2000. [ bib | pdf | Abstract ]
  Douglas N. Arnold, Franco Brezzi, Bernardo Cockburn, and Donatella Marini. Discontinuous Galerkin methods for elliptic problems. In B. Cockburn, G. Karniadakis, and C. Shu, editors, Discontinuous Galerkin methods (Newport, RI, 1999), volume 11 of Lect. Notes Comput. Sci. Eng., pages 89-101. Springer, Berlin, 2000. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Richard S. Falk, and Ragnar Winther. Multigrid in H(div) and H(curl). Numer. Math., 85(2):197-217, 2000. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Arup Mukherjee, and Luc Pouly. Locally adapted tetrahedral meshes using bisection. SIAM J. Sci. Comput., 22(2):431-448, 2000. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Arup Mukherjee. Tetrahedral bisection and adaptive finite elements. In M. Bern, J. Flahery, and M. Luskin, editors, Grid generation and adaptive algorithms (Minneapolis, MN, 1997), volume 113 of IMA Vol. Math. Appl., pages 29-42. Springer, New York, 1999. [ bib | DOI | pdf | Abstract ]
  D. N. Arnold, A. Mukherjee, and L. Pouly. Adaptive finite elements and colliding black holes. In D. Griffiths, D. Higham, and G. Watson, editors, Numerical analysis 1997 (Dundee), volume 380 of Pitman Res. Notes Math. Ser., pages 1-15. Longman, Harlow, 1998. [ bib | pdf | Abstract ]
  D. N. Arnold, R. S. Falk, and R. Winther. Multigrid preconditioning in H(div) on non-convex polygons. Comput. Appl. Math., 17(3):303-315, 1998. [ bib | pdf | Abstract ]
  Stephan M. Alessandrini, Douglas N. Arnold, Richard S. Falk, and Alexandre L. Madureira. Dimensional reduction for plates based on mixed variational principles. In Shells (Santiago de Compostela, 1997), volume 105 of Cursos Congr. Univ. Santiago de Compostela, pages 25-28. Univ. Santiago de Compostela, Santiago de Compostela, 1997. [ bib | pdf | Abstract ]
  D. N. Arnold, R. S. Falk, and R. Winther. Preconditioning discrete approximations of the Reissner-Mindlin plate model. In P. Bjørstad, M. Espedal, and D. Keyes, editors, Ninth International Conference on Domain Decomposition Methods, pages 215-221. DDM.org, 1996. [ bib | pdf | Abstract ]
  D. N. Arnold, R. S. Falk, and R. Winther. Preconditioning in H(div) and applications. In P. Bjørstad, M. Espedal, and D. Keyes, editors, Ninth International Conference on Domain Decomposition Methods, pages 12-19. DDM.org, 1996. [ bib | pdf | Abstract ]
  Stephen M. Alessandrini, Douglas N. Arnold, Richard S. Falk, and Alexandre L. Madureira. Derivation and justification of plate models by variational methods. In M. Fortin, editor, Plates and shells (Québec, QC, 1996), volume 21 of CRM Proc. Lecture Notes, pages 1-20. Amer. Math. Soc., Providence, RI, 1999. [ bib | pdf | Abstract ]
  Douglas N. Arnold. Computer-aided instruction. In Encarta Encyclopedia. Microsoft, 1997. [ bib | pdf | Abstract ]
  Douglas N. Arnold, Richard S. Falk, and Ragnar Winther. Preconditioning discrete approximations of the Reissner-Mindlin plate model. RAIRO Modél. Math. Anal. Numér., 31(4):517-557, 1997. [ bib | pdf | Abstract ]
  Douglas N. Arnold, Richard S. Falk, and R. Winther. Preconditioning in H(div) and applications. Math. Comp., 66(219):957-984, 1997. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Richard S. Falk. Analysis of a linear-linear finite element for the Reissner-Mindlin plate model. Math. Models Methods Appl. Sci., 7(2):217-238, 1997. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Xiaobo Liu. Interior estimates for a low order finite element method for the Reissner-Mindlin plate model. Adv. Comput. Math., 7(3):337-360, 1997. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Franco Brezzi. The partial selective reduced integration method and applications to shell problems. Comput. Structures, 64:879-880, 1997. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Franco Brezzi. Locking-free finite element methods for shells. Math. Comp., 66(217):1-14, 1997. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Richard S. Falk. Asymptotic analysis of the boundary layer for the Reissner-Mindlin plate model. SIAM J. Math. Anal., 27(2):486-514, 1996. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Xiao Bo Liu. Local error estimates for finite element discretizations of the Stokes equations. RAIRO Modél. Math. Anal. Numér., 29(3):367-389, 1995. [ bib | pdf | Abstract ]
  Douglas N. Arnold. On nonconforming linear-constant elements for some variants of the Stokes equations. Istit. Lombardo Accad. Sci. Lett. Rend. A, 127(1):83-93 (1994), 1993. [ bib | pdf | Abstract ]
  Douglas N. Arnold and Franco Brezzi. Some new elements for the Reissner-Mindlin plate model. In C. Baiocchi and J.-L. Lions, editors, Boundary value problems for partial differential equations and applications, volume 29 of RMA Res. Notes Appl. Math., pages 287-292. Masson, Paris, 1993. [ bib | pdf | Abstract ]
  Douglas N. Arnold and Jinshui Qin. Quadratic velocity/linear pressure Stokes elements. In R. Vichnevetsky, D. Knight, and G. Richter, editors, Advances in Computer Methods for Partial Differential Equations-VII, pages 28-34. IMACS, 1992. [ bib | pdf | Abstract ]
  Douglas N. Arnold. Innovative finite element methods for plates. Mat. Apl. Comput., 10(2):77-88, 1991. [ bib | pdf | Abstract ]
  Douglas N. Arnold. Mixed finite element methods for elliptic problems. Comput. Methods Appl. Mech. Engrg., 82(1-3):281-300, 1990. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Richard S. Falk. The boundary layer for the Reissner-Mindlin plate model. SIAM J. Math. Anal., 21(2):281-312, 1990. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Richard Falk. Edge effects in the Reissner-Mindlin plate theory. In A. Noor, T. Belytschko, and J. Simo, editors, Analytical and Computational Models for Shells, pages 71-90. American Society of Mechanical Engineers, 1989. [ bib | pdf | Abstract ]
  Douglas N. Arnold and Patrick J. Noon. Coercivity of the single layer heat potential. J. Comput. Math., 7(2):100-104, 1989. [ bib | pdf | Abstract ]
  Douglas N. Arnold and Richard S. Falk. A uniformly accurate finite element method for the Reissner-Mindlin plate. SIAM J. Numer. Anal., 26(6):1276-1290, 1989. [ bib | DOI | pdf | Abstract ]
  R. S.-C. Cheng and D. N. Arnold. The delta-trigonometric method using the single-layer potential representation. J. Integral Equations Appl., 1(4):517-547, 1988. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, L. Ridgway Scott, and Michael Vogelius. Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon. Ann. Scuola Norm. Sup. Pisa Cl. Sci. (4), 15(2):169-192, 1988. [ bib | pdf | Abstract ]
  Douglas N. Arnold and Richard S. Falk. A new mixed formulation for elasticity. Numer. Math., 53(1-2):13-30, 1988. [ bib | DOI | pdf | Abstract ]
  D. N. Arnold and P. J. Noon. Boundary integral equations of the first kind for the heat equation. In C. Brebbia, W. Wendland, and G. Kuhn, editors, Boundary elements IX, Vol. 3 (Stuttgart, 1987), pages 213-229. Comput. Mech., Southampton, 1987. [ bib | pdf | Abstract ]
  Douglas N. Arnold and Richard S. Falk. Well-posedness of the fundamental boundary value problems for constrained anisotropic elastic materials. Arch. Rational Mech. Anal., 98(2):143-165, 1987. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Richard S. Falk. Continuous dependence on the elastic coefficients for a class of anisotropic materials. Technical Report 165, Institute for Mathematics & its Applications, 1985. [ bib | pdf | Abstract ]
  Douglas N. Arnold and Wolfgang L. Wendland. The convergence of spline collocation for strongly elliptic equations on curves. Numer. Math., 47(3):317-341, 1985. [ bib | DOI | pdf | Abstract ]
  D. N. Arnold and F. Brezzi. Mixed and nonconforming finite element methods: implementation, postprocessing and error estimates. RAIRO Modél. Math. Anal. Numér., 19(1):7-32, 1985. [ bib | pdf | Abstract ]
  D. N. Arnold, F. Brezzi, and M. Fortin. A stable finite element for the Stokes equations. Calcolo, 21(4):337-344 (1985), 1984. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold. A new mixed formulation for the numerical solution of elasticity problems. In R. Vichnevetsky and R. Stepleman, editors, Advances in Computer Methods for Partial Differential Equations-V, pages 353-356. IMACS, 1984. [ bib | pdf | Abstract ]
  Douglas N. Arnold. The effect of the test functions on the convergence of spline projection methods for singular integral equations. In A. Gerasoulis and R. Vichnevetsky, editors, Numerical Solution of Singular Integral Equations, pages 1-4. IMACS, 1984. [ bib | pdf | Abstract ]
  Douglas N. Arnold, Franco Brezzi, and Jim Douglas, Jr. PEERS: a new mixed finite element for plane elasticity. Japan J. Appl. Math., 1(2):347-367, 1984. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold, Jim Douglas, Jr., and Chaitan P. Gupta. A family of higher order mixed finite element methods for plane elasticity. Numer. Math., 45(1):1-22, 1984. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Jukka Saranen. On the asymptotic convergence of spline collocation methods for partial differential equations. SIAM J. Numer. Anal., 21(3):459-472, 1984. [ bib | DOI | pdf | Abstract ]
  D. N. Arnold, I. Babuška, and J. Osborn. Finite element methods: principles for their selection. Comput. Methods Appl. Mech. Engrg., 45(1-3):57-96, 1984. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Wolfgang L. Wendland. On the asymptotic convergence of collocation methods. Math. Comp., 41(164):349-381, 1983. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold. A spline-trigonometric Galerkin method and an exponentially convergent boundary integral method. Math. Comp., 41(164):383-397, 1983. [ bib | DOI | pdf | Abstract ]
  D. N. Arnold, I. Babuška, and J. Osborn. Selection of finite element methods. In S. Atluri, R. Gallagher, and O. Zienkiewicz, editors, Hybrid and mixed finite element methods (Atlanta, Ga., 1981), Wiley-Intersci. Pub., pages 433-451. Wiley, New York, 1983. [ bib | pdf | Abstract ]
  D. N. Arnold and W. L. Wendland. Collocation versus Galerkin procedures for boundary integral methods. In C. Brebbia, editor, Boundary element methods in engineering (Southampton, 1982), pages 18-33. Springer, Berlin, 1982. [ bib | pdf | Abstract ]
  Douglas N. Arnold. An interior penalty finite element method with discontinuous elements. SIAM J. Numer. Anal., 19(4):742-760, 1982. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold and Ragnar Winther. A superconvergent finite element method for the Korteweg-de Vries equation. Math. Comp., 38(157):23-36, 1982. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold. Discretization by finite elements of a model parameter dependent problem. Numer. Math., 37(3):405-421, 1981. [ bib | DOI | pdf | Abstract ]
  Douglas N. Arnold. Robustness of finite element methods for a model parameter dependent problem. In R. Vichnevetsky and R. Stepleman, editors, Advances in Computer Methods for Partial Differential Equations-IV, pages 18-22. IMACS, 1981. [ bib | pdf | Abstract ]
  Douglas N. Arnold, Jim Douglas, Jr., and Vidar Thomée. Superconvergence of a finite element approximation to the solution of a Sobolev equation in a single space variable. Math. Comp., 36(153):53-63, 1981. [ bib | DOI | pdf | Abstract ]
  D. N. Arnold and J. Douglas, Jr. Superconvergence of the Galerkin approximation of a quasilinear parabolic equation in a single space variable. Calcolo, 16(4):345-369, 1979. [ bib | DOI | pdf | Abstract ]

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Modified December 21, 2013 by Douglas N. Arnold