Research Group on
Numerical Methods for PDEs
and Related Analysis Topics
Department of Mathematics, FCEyN, University of Buenos Aires
Publications
M. G. Armentano and C. Padra, A posteriori error estimates for the Steklov eigenvalue problem, to appear in Applied Numerical Mathematics, vol 58, Issue 5, pp 593-601 (2008)
G. Acosta, Th. Apel, R. G. Durán and A. L. Lombardi, Anisotropic error estimates for an interpolant defined via moments. Computing 82, 1-9, 2008.
R. G. Durán and A. L. Lombardi, Error estimates for the Raviart-Thomas interpolation under the maximum angle condition. SIAM J. Numer. Anal. 46, 1442-1453, 2008.
G. Acosta, M. G. Armentano, R. G. Durán and A. L. Lombardi, Finite element approximations in a non-Lipschitz domain. SIAM J. Numer. Anal. 45, 277-295, 2007.
R. G. Durán, Error estimates for anisotropic finite elements and applications, Proceedings of International Congress of Mathematicians, Madrid 2006, Volume III, pp. 1181-1200.
G. Acosta, G. Monzón, Interpolation error estimates in W{1,p} for degenerate Q1 isoparametric elements. Numer. Math. , 104, pp 129-150, 2006.
G. Acosta, M. Graña and J. P. Pinasco, Condition Numbers and Scale Free Graphs. Eur. Phys. J. B 53, 381-385 2006.
R. G. Durán, Ariel L. Lombardi, Finite element approximation of convection diffusion problems using graded meshes, Applied Numerical Mathematics 56, 1314-1325, 2006.
R. G. Durán and A. L. Lombardi, Error estimates on anisotropic Q1 elements for functions in weighted Sobolev spaces, Math. Comp. 74, 1679-1706, 2005.
R. G. Durán, The inf-sup condition for the Stokes equations: A constructive approach in general domains, Mathematisches Forschungsinstitut Oberwolfach, Workshop on Gemischte und nicht-standard Finite-Elemente-Methoden mit Anwendungen, Extended abstract, Report No. 5/2005, pp. 270-272.
María G. Armentano, The effect of reduced integration in the Steklov eigenvalue problem, Mathematical Modelling and Numerical Analysis (M2AN), vol 38, no 1, pp 27-36 (2004).
M. G. Armentano and R. G. Durán, Asymptotic lower bounds for eigenvalues by nonconforming finite element methods. Electronic Trans. Numer. Anal. 17, 93-101, 2004.
M. G. Armentano and R. G. Durán, Mass lumping or not mass lumping in eigenvalue problems, Numerical Methods for Partial Differential Equations 19(5), 2003, 653--664.
R. G. Durán, E. Hernández, L. Hervella Nieto, E. Liberman and R. Rodríguez, Error estimates for low-order isoparametric quadrilateral finite elements for plates. SIAM J. Numer. Anal. 41(5), 1751-1772, 2003.
R. G. Durán, C. Padra and R. Rodríguez, A posteriori error estimates for the finite element approximation of eigenvalue problems. Math. Mod. Meth. Appl. Sci. 13(8), 1219-1229, 2003.
G. Acosta, J. Fernández Bonder, P. Groisman, J. D. Rossi, Simultaneous vs. non-simultaneous blow up in numerical approximations of a parabolic system with nonlinear boundary conditions, M2AN Math. Model. Numer. Anal. 36(1), 55-68, 2002. .
G. Acosta, J. Fernández Bonder, P. Groisman, J. D. Rossi, Numerical approximation of a parabolic problem with a nonlinear boundary condition in several space dimensions, Discrete and continuous dynamical systems - serie B 2(2), 279-294, 2002.
G. Acosta, R. G. Durán, J. D. Rossi, An adaptive time step procedure for a parabolic problem with blow up, Computing 68(4), 343-373, 2002.
G. Acosta, Lagrange and average interpolation over 3D anisotropic elements, Jour. on Comp. and Applied Math. 135, 2001, 91-109.
M. G. Armentano, Error estimates in Sobolev spaces for moving least square approximations, SIAM Jour. Numer. Anal. 39(1), 2001, 38-51.
M. G. Armentano and R. G. Durán, Error estimates for moving least square approximations, Applied Numerical Mathematics, 37, 397-416, 2001.
G. C. Buscaglia, R. G. Durán, E. A. Fancello,R. A. Feijóo and C. Padra, An adaptive finite element approach for frictionless contact problems, Int. J. Numer. Meth. Engng. 50, 395-418, 2001.
G. Acosta, J. Fernández Bonder, J. D. Rossi. Stable manifold approximation for the heat equation with nonlinear boundary conditions. J. Dynam. Differential Equations, 12 (3) (2000), pp. 557-578.
G. Acosta and R. G. Durán , The maximum angle condition for mixed and non conforming elements: Application to the Stokes equations, SIAM J. Numer. Anal. 37, 18-36, 2000.
G. Acosta and R. G. Durán, Error estimates for $Q_1$ isoparametric elements satisfying a weak angle condition, SIAM J. Numer. Anal. 38, 1073-1088, 2000.
A. Bermúdez, R. G. Durán, R. Rodríguez and J. Solomín, Finite element analysis of a quadratic eigenvalue problem arising in dissipative acoustics, SIAM J. Numer. Anal. 38, 267-291, 2000.
E. Dari , R. G. Durán and C. Padra, Maximum norm error estimators for three dimensional elliptic problems, SIAM J. Numer. Anal. 37(2), 683-700, 2000.
R. G. Durán, L. Hervella Nieto, E. Liberman, R. Rodríguez and J. Solomin, Finite element analysis of the vibration problem of a plate coupled with a fluid, Numer. Math. 86, 591-616, 2000.
D. Boffi, R. G. Durán and L. Gastaldi, A remark on spurious eigenvalues in a square, Applied Mathematics Letters 12, 107-114, 1999.
R. G. Durán, Error estimates for narrow 3-d finite elements, Math. Comp. 68, 187-199, 1999.
R. G. Durán , L. Gastaldi and C. Padra, A posteriori error estimators for mixed approximations of eigenvalue problems, Math. Mod. Meth. Appl. Sci. 9, 1165-1178, 1999.
R.G. Durán , L. Hervella Nieto, E. Liberman, R. Rodríguez and J. Solomin, Approximation of the vibration modes of a plate by Reissner-Mindlin equations, Math. Comp. 68, 1447-1463, 1999.
A. Bermúdez, R. G. Durán and R. Rodríguez, Finite element analysis of compressible and incompressible fluid-solid systems, Math. Comp. 67, 111-136, 1998.
R. G. Durán, J. Etcheverry and J. D. Rossi, Numerical approximation of a parabolic problem with a nonlinear boundary condition, Discrete and Continuous Dynamical Systems 4(3), 497-506, 1998.
A. Bermúdez, R. G. Durán and R. Rodríguez, Finite element solution of incompressible fluid-structure vibration problems. Int. J. Numer. Meth. Engng. 40(8), 1435-1448, 1997.
R. G. Durán and E. Liberman, On the convergence of a triangular mixed finite elementmethod for Reissner-Mindlin plates. Math. Mod. Meth. Appl. Sci. 6(3), 339-352, 1996.
E. Dari, R. G. Durán, C. Padra and V. Vampa, A posteriori error estimators for nonconforming finite element methods. Math. Model. Numer. Anal. (RAIRO) 30(4), 385-400, 1996.
A. Bermúdez, R. G. Durán, M.A. Muschietti, R. Rodríguez and J. Solomin, Finite element vibration analysis of fluid-solid systems without spurious modes. SIAM J. Numer. Anal. 32(4),1280-1295, 1995.
E. Dari, R. G. Durán and C. Padra, Error estimators for nonconforming finite element approximations of the Stokes problem. Math. Comp. 64(211), 1017-1033, 1995.
I. Babuska, R. G. Durán and R. Rodríguez, Analysis of the efficiency of an a-posteriori error estimator for linear triangular finite elements. SIAM J. Numer. Anal. 29, 947-964, 1992.
R. G. Durán and R. Rodríguez, On the asymptotic exactness of Bank-Weiser's estimator. Numer. Math. 62, 297-303, 1992.
R. G. Durán and E. Liberman, On Mixed Finite Element Methods for the Reissner Mindlin Plate Model. Math. Comp. 58(198), 561-573, 1992.
R. G. Durán, M. A. Muschietti and R. Rodríguez, Asymptotically Exact Error Estimators for Rectangular Finite Elements. SIAM J. Numer. Anal. 29(1), 78-88, 1992.
R. G. Durán, M. A. Muschietti and R. Rodríguez, Asymptotically Exact Error Estimators for Rectangular Finite Elements. SIAM J. Numer. Anal. 29(1), 78-88, 1992.
R. G. Durán, The Inf-Sup Condition an Error Estimates for the Arnold-Falk PlateBending Element. Numer. Math. 58(8), 769-778, 1991.
R. G. Durán, A. Ghioldi and N. Wolanski, A Finite Element Method for the Mindlin-Reissner Plate Model. SIAM J. Numer. Anal. 28(4),1004-1014, 1991.
R. G. Durán, M. A. Muschietti and R. Rodríguez, On the Asymptotic Exactness of a Posteriori Error Estimators for Linear Triangular Finite Elements. Numer. Math. 59, 107-127, 1991.
R. G. Durán, Superconvergence for Rectangular Mixed Finite Elements. Numer. Math. 58, 287-298, 1990.
R. G. Durán, Finite Elements in H (curl) with Applications to Elasticity, Numer. Meth. PDE's 6(2), 167-175, 1990.
R. G. Durán and R. H. Nochetto, Weighted Inf-Sup Condition and Pointwise Error Estimates for the Stokes Problem. Math. Comp. 54(189), 63-79, 1990.
R. G. Durán and R. H. Nochetto, Pointwise Accuracy of a Stable Petrov-Galerkin Method for the Stokes Problem. SIAM J. Numer. Anal. 26(6), 1395-1406, 1989.
R. G. Durán, Error Analysis in Lp for Mixed Finite Element Methods for Linear and Quasilinear Elliptic Problems. RAIRO, Model. Math. Numer. Anal. 22(3), 371-387, 1988.
R. G. Durán, R. Nochetto and J. Wang, Sharp Maximum Norm Error Estimates for Finite Element Approximations ofthe Stokes Problem in 2-D. Math. Comp. 51(184), 491-506, 1988.
R. G. Durán, A Note on the Convergence of Linear Finite Elements. SIAM J. Numer. Anal. 25(5), 1032-1036, 1988.
R. G. Durán, On the Approximation of Miscible Displacement in Porous Media bythe Method of Characteristics Combined with a Mixed Method. SIAM J. Numer. Anal. 25(5), 989-1001, 1988
F. Brezzi, J. Douglas, R. G. Durán and M. Fortin, Mixed Finite Elements for Second Order Elliptic Problems in Three Variables. Numer. Math. 51, 137-150, 1987.
R. G. Durán, Quasi-optimal Estimates for Finite Element Approximations Using Orlicz Norms. Math. Comp. 49 (179), 17-23, 1987.
R. G. Durán and F. López García, A right inverse of the divergence for planar Hölder alpha domains. Submitted for publication
R. G. Durán, M. Sanmartino and M. Toschi, Weighted a priori estimates for Poisson equation. To appear in Indiana University Math. Journal.
I. Drelichman and R. G. Durán, Improved Poincaré inequalities with weights. Journal of Mathematical Analysis and Applications 347, 286-293, 2008.
G. Acosta, R. G. Durán and A. L. Lombardi, Weighted Poincaré and Korn inequalities for Hölder domains, Math. Meth. Appl. Sci..29 (4), 387-400, 2006.
G. Acosta, R. G. Durán and M. A. Muschietti, Solutions of the divergence operator on John domains. Advances in Mathematics, 206(2), 373-401, 2006
G. Acosta, M. A. Armentano, R. G. Durán, A. L. Lombardi, Nonhomogeneous Neumann problem for the Poisson equation in domains with an external cusp, J. Math. Anal. Appl. 310 (2), 397-411, (2005).
R. G. Durán and M. A. Muschietti, The Korn inequality for Jones domains, Electronic Jour. Diff. Eqs. Vol. 2004(2004), No. 127, pp. 1-10.
G. Acosta and R. G. Durán, An optimal Poincaré inequality in L1 for convex domains, Proc. AMS 132(1), 195-202, 2003.
R. G. Durán and M. A. Muschietti, On the traces of W2,p for a Lipschitz domain, Revista Matemática Complutense XIV(2), 371-377, 2001.
R. G. Durán and M. A. Muschietti, An explicit right inverse of the divergence operator which is continuous in weighted norms, Studia Mathematica 148(3), 207-219, 2001.
J. Alvárez and R. G. Durán, On the Lp Boundedness of Pseudodifferential Operators with Discontinuous Symbols. Proc. AMS 104(1), 165-168, 1988.
R. G. Durán, Parabolic Maximal Functions and Potentials of Distributions in Hp. J. Math. Anal. Appl. 100(1), 130-154, 1984.
R. G. Durán, On Polynomial Approximation in Sobolev Spaces. SIAM J. Numer.Anal. 20(5), 98-988, 1983