Edit Profile Babuška, Ivo Compute Distance To: Compute Author ID: babuska.ivo-m Published as: Babuska, I.; Babuska, Ivo; Babuska, Ivo M.; Babusǩa, I.; Babuška, I.; Babuška, Ivo; Babuška, Ivo M.; Babuška, J. Homepage: https://users.ices.utexas.edu/~babuska/ External Links: MGP · Wikidata · dblp · GND · MacTutor Documents Indexed: 392 Publications since 1954, including 14 Books Biographic References: 9 Publications all top 5 Co-Authors 72 single-authored 39 Strouboulis, Theofanis 23 Osborn, John E. 22 Guo, Benqi 18 Banerjee, Uday 16 Gangaraj, S. K. 16 Tempone, Raúl F. 13 Oden, John Tinsley 13 Rheinboldt, Werner C. 12 Szabó, Barna Aladar 11 Suri, Manil 11 Upadhyay, Chandra Shekhar 10 Vitásek, Emil 9 Copps, K. 8 Ihlenburg, Frank 7 Nobile, Fabio 7 Práger, Milan 6 Andersson, Börje 6 Miller, Alan D. 6 Pitkäranta, Juhani 6 Sauter, Stefan A. 6 Zhang, Lin 6 Zhang, Qinghui 5 Datta, Dibyendu K. 5 Li, Likang 5 Lipton, Robert P. 5 Liu, Kangman 5 Oh, Hae-Soo 5 Schwab, Christoph 5 Vogelius, Michael S. 4 Elman, Howard C. 4 Melenk, Jens Markus 4 Nistor, Victor 4 Rodríguez, Rodolfo 3 Bieterman, Michael B. 3 Chen, Qi 3 Chleboun, Jan 3 Demkowicz, Leszek F. 3 Flaherty, Joseph E. 3 Gui, Wangsheng 3 Morgan, Richard C. 3 von Petersdorff, Tobias 3 Výborný, Rudolf 3 Wang, Delin 2 Arnold, Douglas Norman 2 Aziz, A. Kadir 2 Baumann, Carlos Erik 2 Bouillard, Philippe 2 Deraemaeker, Arnaud 2 Dowding, Kevin J. 2 Duarte, C. A. M. 2 Duarte, Carlos Armando 2 Feng, Yusheng 2 Gago, J. 2 Gatica, Gabriel N. 2 Gupta, Varun 2 Hidajat, Realino 2 Hills, Richard G. 2 Hlaváček, Ivan 2 Hughes, Thomas J. R. 2 Janik, Tadeusz J. 2 Kautsky, Jaroslav 2 Kellogg, Bruce 2 Kergrene, Kenan 2 Kroupa, František 2 Li, Yiwei 2 Majer, V. R. 2 Makridakis, Charalambos G. 2 Martinsson, Per-Gunnar 2 Mathur, A. N. 2 Motamed, Mohammad 2 Paez, Thomas L. 2 Rank, Ernst 2 Red-Horse, John R. 2 Sawlan, Zaid 2 Scavino, Marco 2 Silva, Renato S. 2 Stephan, Ernst Peter 2 Stuebner, Michael 2 Szymczak, William G. 2 Tarfulea, Nicolae 2 Zhang, Zhimin 2 Zienkiewicz, Olgierd Cecil 2 Zouraris, Georgios E. 1 Actis, Ricardo L. 1 Adjerid, Slimane 1 Ainsworth, Mark 1 Babušková, Renata 1 Bajaj, Chanderjit L. 1 Bass, Jon M. 1 Bazilevs, Yuri 1 Belytschko, Ted Bohdan 1 Biduat, L. 1 Browne, James C. 1 Caloz, Gabriel 1 Chandra, Jagdish 1 Chatzipantelidis, Panagiotis 1 Chayapathy, Bidar K. 1 Chen, Jiuhua 1 Ciarlet, Philippe Gaston 1 Craig, Anthony ...and 81 more Co-Authors all top 5 Serials 75 Computer Methods in Applied Mechanics and Engineering 36 SIAM Journal on Numerical Analysis 29 International Journal for Numerical Methods in Engineering 25 Numerische Mathematik 17 Aplikace Matematiky 15 Mathematics of Computation 9 Časopis Pro Pěstování Matematiky 9 Numerical Methods for Partial Differential Equations 9 M\(^3\)AS. Mathematical Models & Methods in Applied Sciences 8 SIAM Journal on Mathematical Analysis 6 Archives of Mechanics 6 Journal of Computational and Applied Mathematics 6 Finite Elements in Analysis and Design 5 Zeitschrift für Angewandte Mathematik und Mechanik (ZAMM) 5 Czechoslovak Mathematical Journal 4 Computers & Mathematics with Applications 4 Commentationes Mathematicae Universitatis Carolinae 3 Computers and Structures 3 Journal of Computational Physics 3 Wissenschaftliche Zeitschrift der Hochschule für Architektur und Bauwesen Weimar 3 Communications in Applied Numerical Methods 3 Computational Mechanics 3 SIAM Review 3 SIAM Journal on Scientific Computing 2 Computing 2 Applied Numerical Mathematics 2 RAIRO. Modélisation Mathématique et Analyse Numérique 2 Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2 Advances in Computational Mathematics 2 Computer Assisted Mechanics and Engineering Sciences 2 Czechoslovak Journal of Physics 2 International Journal of Numerical Analysis and Modeling 1 Acta Mechanica 1 Applicable Analysis 1 Archive for Rational Mechanics and Analysis 1 Mathematical Methods in the Applied Sciences 1 ACM Transactions on Mathematical Software 1 Annales Polonici Mathematici 1 BIT 1 Journal of Approximation Theory 1 Rendiconti del Seminario Matematico 1 Advances in Applied Mathematics 1 SIAM Journal on Scientific and Statistical Computing 1 Journal of Complexity 1 Mathematical and Computer Modelling 1 IMPACT of Computing in Science and Engineering 1 Applications of Mathematics 1 Bulletin de l’Académie Polonaise des Sciences, Série des Sciences Techniques 1 International Journal of Computer Mathematics 1 Pokroky Matematiky, Fyziky & Astronomie 1 U.S.S.R. Computational Mathematics and Mathematical Physics 1 Wissenschaftliche Zeitschrift der Technischen Universität Dresden 1 Advances in Engineering Software 1 Tatra Mountains Mathematical Publications 1 Communications in Numerical Methods in Engineering 1 Mathematical Modelling and Scientific Computing 1 Computing and Visualization in Science 1 Comptes Rendus de l’Académie des Sciences. Série II. Fascicule b. Mécanique, Physique, Astronomie 1 Multiscale Modeling & Simulation 1 International Journal of Computational Methods 1 Acta Numerica 1 European Series in Applied and Industrial Mathematics (ESAIM): Mathematical Modelling and Numerical Analysis 1 Acta Facultatis Rerum Naturalium Universitatis Comenianae. Mathematica 1 The IMA Volumes in Mathematics and its Applications 1 Lecture Notes in Computational Science and Engineering all top 5 Fields 261 Numerical analysis (65-XX) 157 Partial differential equations (35-XX) 138 Mechanics of deformable solids (74-XX) 26 Ordinary differential equations (34-XX) 20 Fluid mechanics (76-XX) 14 Approximations and expansions (41-XX) 13 General and overarching topics; collections (00-XX) 10 Probability theory and stochastic processes (60-XX) 8 Functional analysis (46-XX) 6 History and biography (01-XX) 5 Statistics (62-XX) 5 Computer science (68-XX) 4 Operator theory (47-XX) 4 Classical thermodynamics, heat transfer (80-XX) 3 Calculus of variations and optimal control; optimization (49-XX) 3 Mechanics of particles and systems (70-XX) 2 Functions of a complex variable (30-XX) 2 Potential theory (31-XX) 1 Mathematical logic and foundations (03-XX) 1 Special functions (33-XX) 1 Dynamical systems and ergodic theory (37-XX) 1 Integral equations (45-XX) 1 Optics, electromagnetic theory (78-XX) 1 Statistical mechanics, structure of matter (82-XX) 1 Biology and other natural sciences (92-XX) Publications by Year all cited Publications top 5 cited Publications Citations contained in zbMATH 319 Publications have been cited 13,671 times in 7,486 Documents Cited by ▼ Year ▼ The partition of unity finite element method: basic theory and applications. Zbl 0881.65099Melenk, J. M.; Babuška, Ivo 809 1996 The partition of unity method. Zbl 0949.65117Babuška, I.; Melenk, J. M. 618 1997 The finite element method with Lagrangian multipliers. Zbl 0258.65108Babuška, Ivo 523 1973 Error estimates for adaptive finite element computations. Zbl 0398.65069Babuška, Ivo; Rheinboldt, W. C. 414 1978 A-posteriori error estimates for the finite element method. Zbl 0396.65068Babuška, Ivo; Rheinboldt, W. C. 349 1978 A stochastic collocation method for elliptic partial differential equations with random input data. Zbl 1151.65008Babuška, Ivo; Nobile, Fabio; Tempone, Raúl 323 2007 Error-bounds for finite element method. Zbl 0214.42001Babuška, Ivo 312 1971 Galerkin finite element approximations of stochastic elliptic partial differential equations. Zbl 1080.65003Babuska, Ivo; Tempone, Raúl; Zouraris, Georgios E. 303 2004 The generalized finite element method. Zbl 0997.74069Strouboulis, T.; Copps, K.; Babuška, I. 300 2001 Finite element analysis. Zbl 0792.73003Szabó, Barna; Babuška, Ivo 255 1991 Eigenvalue problems. Zbl 0875.65087Babuška, Ivo; Osborn, J. 248 1991 The design and analysis of the generalized finite element method. Zbl 0983.65127Strouboulis, T.; Babuška, I.; Copps, K. 238 2000 Finite element solution of the Helmholtz equation with high wave number. I: The \(h\)-version of the FEM. Zbl 0838.65108Ihlenburg, Frank; Babuška, Ivo 207 1995 A discontinuous \(hp\) finite element method for diffusion problems. Zbl 0926.65109Oden, J. Tinsley; Babuška, Ivo; Baumann, Carlos Erik 187 1998 Special finite element methods for a class of second order elliptic problems with rough coefficients. Zbl 0807.65114Babuška, Ivo; Caloz, Gabriel; Osborn, John E. 179 1994 The h-p version of the finite element method with quasiuniform meshes. Zbl 0623.65113Babuška, I.; Suri, Manil 165 1987 On the angle condition in the finite element method. Zbl 0324.65046Babuška, Ivo; Aziz, A. K. 163 1976 The p-version of the finite element method. Zbl 0487.65059Babuška, Ivo; Szabo, B. A.; Katz, I. N. 150 1981 The finite element method for elliptic equations with discontinuous coefficients. Zbl 0199.50603Babuška, Ivo 150 1970 A generalized finite element method for solving the Helmholtz equation in two dimensions with minimal pollution. Zbl 0863.73055Babuška, Ivo; Ihlenburg, Frank; Paik, Ellen T.; Sauter, Stefan A. 147 1995 The finite element methods and its reliability. Zbl 0995.65501Babuška, Ivo; Strouboulis, Theofanis 146 2001 Solution of stochastic partial differential equations using Galerkin finite element techniques. Zbl 1075.65006Deb, Manas K.; Babuška, Ivo M.; Oden, J. Tinsley 143 2001 Survey lectures on the mathematical foundations of the finite element method. With the collaboration of G. Fix and R. B. Kellogg. Zbl 0268.65052Babuška, Ivo; Aziz, A. K. 138 1972 Finite element solution of the Helmholtz equation with high wave number. II: The \(h-p\) version of the FEM. Zbl 0884.65104Ihlenburg, Frank; Babuška, Ivo 136 1997 Generalized finite element methods: Their performance and their relation to mixed methods. Zbl 0528.65046Babuška, Ivo; Osborn, J. E. 136 1983 Survey of meshless and generalized finite element methods: A unified approach. Zbl 1048.65105Babuška, Ivo; Banerjee, Uday; Osborn, John E. 132 2003 The \(p\) and \(h-p\) versions of the finite element method, basic principles and properties. Zbl 0813.65118Babuška, Ivo; Suri, Manil 122 1994 \(n\)-widths, sup-infs, and optimality ratios for the \(k\)-version of the isogeometric finite element method. Zbl 1227.65093Evans, John A.; Bazilevs, Yuri; Babuška, Ivo; Hughes, Thomas J. R. 119 2009 Direct and inverse error estimates for finite elements with mesh refinements. Zbl 0423.65057Babuška, Ivo; Kellogg, R. B.; Pitkäranta, J. 115 1979 Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers? Zbl 0894.65050Babuška, Ivo M.; Sauter, Stefan A. 114 1997 The optimal convergence rate of the p-version of the finite element method. Zbl 0637.65103Babuška, I.; Suri, Manil 113 1987 The h-p version of the finite element method. I. The basic approximation results. Zbl 0634.73058Guo, B.; Babuška, I. 113 1986 A stochastic collocation method for elliptic partial differential equations with random input data. Zbl 1226.65004Babuška, Ivo; Nobile, Fabio; Tempone, Raúl 107 2010 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. Zbl 0593.65064Babuška, Ivo; Miller, A. 104 1987 The finite element method with penalty. Zbl 0299.65057Babuška, Ivo 102 1973 Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation. Zbl 1087.65004Babuška, Ivo; Tempone, Raúl; Zouraris, Georgios E. 101 2005 The generalized finite element method: An example of its implementation and illustration of its performance. Zbl 0955.65080Strouboulis, T.; Copps, K.; Babuška, I. 98 2000 Nonconforming elements in the finite element method with penalty. Zbl 0237.65066Babuška, Ivo; Zlámal, Milos 97 1973 Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions. Zbl 0957.65098Deraemaeker, Arnaud; Babuška, Ivo; Bouillard, Philippe 95 1999 Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers? Zbl 0956.65095Babuska, Ivo M.; Sauter, Stefan A. 92 2000 On locking and robustness in the finite element method. Zbl 0763.65085Babuška, Ivo; Suri, Manil 89 1992 The p- and h-p versions of the finite element method. An overview. Zbl 0731.73078Babuška, Ivo; Suri, Manil 88 1990 Validation of a posteriori error estimators by numerical approach. Zbl 0811.65088Babuška, I.; Strouboulis, T.; Upadhyay, C. S.; Gangaraj, S. K.; Copps, K. 87 1994 Finite element-Galerkin approximation of the eigenvalues and eigenvectors of selfadjoint problems. Zbl 0675.65108Babuška, I.; Osborn, J. E. 86 1989 The post-processing approach in the finite element method. I. Calculation of displacements, stresses and other higher derivatives of the displacements. Zbl 0535.73052Babuška, Ivo; Miller, A. 85 1984 Dispersion analysis and error estimation of Galerkin finite element methods for the Helmholtz equation. Zbl 0851.73062Ihlenburg, Frank; Babuška, Ivo 81 1995 Stable generalized finite element method (SGFEM). Zbl 1239.74093Babuška, I.; Banerjee, U. 77 2012 The h-p version of the finite element method for domains with curved boundaries. Zbl 0655.65124Babuška, I.; Guo, B. Q. 77 1988 Analysis of mixed methods using mesh dependent norms. Zbl 0472.65083Babuška, Ivo; Osborn, J.; Pitkäranta, J. 76 1980 Locking effects in the finite element approximation of elasticity problems. Zbl 0762.65057Babuška, Ivo; Suri, Manil 70 1992 Regularity of the solution of elliptic problems with piecewise analytic data. I: Boundary value problems for linear elliptic equations of second order. Zbl 0647.35021Babuška, I.; Guo, B. Q. 70 1988 The h, p and h-p versions of the finite element method in 1 dimension. I. The error analysis of the p-version. Zbl 0614.65088Gui, W.; Babuška, I. 70 1986 The h-p version of the finite element method. II. General results and applications. Zbl 0634.73059Guo, B.; Babuška, I. 68 1986 Efficient preconditioning for the \(p\)-version finite element method in two dimensions. Zbl 0754.65083Babuška, I.; Craig, A.; Mandel, J.; Pitkäranta, J. 67 1991 Reliable and robust a posteriori error estimation for singularly perturbed reaction-diffusion problems. Zbl 0948.65114Ainsworth, Mark; Babuska, Ivo 66 1998 The h, p and h-p versions of the finite element method in 1 dimension. III. The adaptive h-p version. Zbl 0614.65090Gui, W.; Babuška, I. 66 1986 On solving elliptic stochastic partial differential equations. Zbl 1019.65010Babuška, Ivo; Chatzipantelidis, Panagiotis 65 2002 Damage analysis of fiber composites. I: Statistical analysis of fiber scale. Zbl 0956.74048Babuška, Ivo; Andersson, Börje; Smith, Paul J.; Levin, Klas 62 1999 The post-processing approach in the finite element method. II. The calculation of stress intensity factors. Zbl 0535.73053Babuška, Ivo; Miller, A. 62 1984 Error estimates for the combined h and p versions of the finite element method. Zbl 0487.65058Babuška, Ivo; Dorr, Milo R. 61 1981 Generalized finite element methods – main ideas, results and perspective. Zbl 1081.65107Babuška, Ivo; Banerjee, Uday; Osborn, John E. 60 2004 The generalized finite element method for Helmholtz equation: theory, computation, and open problems. Zbl 1120.76044Strouboulis, Theofanis; Babuška, Ivo; Hidajat, Realino 59 2006 The h, p and h-p versions of the finite element method in 1 dimension. II. The error analysis of the h- and h-p versions. Zbl 0614.65089Gui, W.; Babuška, I. 57 1986 Accuracy estimates and adaptive refinements in finite element computations. Lectures presented at the international conference held in Lisbon, June 1984. Zbl 0663.65001Babuška, I. (ed.); Zienkiewicz, O. C. (ed.); Gago, J. (ed.); de Arantes Oliveira, E. R. (ed.) 56 1986 Feedback and adaptive finite element solution of one-dimensional boundary value problems. Zbl 0574.65098Babuška, Ivo; Vogelius, M. 54 1984 Optimal local approximation spaces for generalized finite element methods with application to multiscale problems. Zbl 1229.65195Babuska, Ivo; Lipton, Robert 53 2011 Approximation properties of the \(h\)-\(p\) version of the finite element method. Zbl 0882.65096Babuška, Ivo; Guo, B. Q. 53 1996 Approximate optimal points for polynomial interpolation of real functions in an interval and in a triangle. Zbl 0862.65006Chen, Qi; Babuška, Ivo 53 1995 Numerical processes in differential equations. Zbl 0156.16003Babuška, Ivo; Práger, Milan; Vitásek, Emil 53 1966 The post-processing approach in the finite element method. III. A posteriori error estimates and adaptive mesh selection. Zbl 0571.73074Babuška, Ivo; Miller, A. 51 1984 Mixed-hybrid finite element approximations of second-order elliptic boundary-value problems. Zbl 0382.65056Babuška, Ivo; Oden, J. T.; Lee, J. K. 49 1977 Generalized finite element method using mesh-based handbooks: application to problems in domains with many voids. Zbl 1054.74059Strouboulis, Theofanis; Zhang, Lin; Babuška, Ivo 47 2003 A discontinuous \(hp\) finite element method for diffusion problems: 1-D analysis. Zbl 0940.65076Babuška, I.; Baumann, C. E.; Oden, J. T. 45 1999 Computer-based proof of the existence of superconvergence points in the finite element method; superconvergence of the derivatives in finite element solutions of Laplace’s, Poisson’s, and the elasticity equations. Zbl 0854.65089Babuška, Ivo; Strouboulis, T.; Upadhyay, C. S.; Gangaraj, S. K. 43 1996 A posteriori estimation and adaptive control of the pollution error in the \(h\)-version of the finite element method. Zbl 0844.65078Babuška, Ivo; Strouboulis, T.; Upadhyay, C. S.; Gangaraj, S. K. 42 1995 Analysis of optimal finite-element meshes in \(R^1\). Zbl 0431.65055Babuška, Ivo; Rheinboldt, W. C. 42 1979 A residual-based a posteriori error estimator for the Stokes-Darcy coupled problem. Zbl 1410.76148Babuška, Ivo; Gatica, Gabriel N. 41 2010 A comparison of approximate boundary conditions and infinite element methods for exterior Helmholtz problems. Zbl 0962.76055Shirron, Joseph J.; Babuška, Ivo 41 1998 On the rates of convergence of the finite element method. Zbl 0498.65050Babuška, Ivo; Szabo, Barna 41 1982 Finite element method for domains with corners. Zbl 0224.65031Babuška, Ivo 41 1970 Continuous dependence of eigenvalues on the domain. Zbl 0137.32302Babuška, Ivo; Vyborny, R. 41 1965 Can a finite element method perform arbitrarily badly? Zbl 0940.65086Babuska, Ivo; Osborn, John E. 40 2000 Benchmark computation and performance evaluation for a rhombic plate bending problem. Zbl 0675.73041Babuška, Ivo; Scapolla, Terenzio 40 1989 A posteriori error analysis of finite element solutions for one- dimensional problems. Zbl 0487.65060Babuška, Ivo; Rheinboldt, Werner C. 39 1981 Direct and inverse approximation theorems for the \(p\)-version of the finite element method in the framework of weighted Besov spaces. I: Approximability of functions in the weighted Besov spaces. Zbl 1008.65078Babuška, Ivo; Guo, Benqi 38 2001 Adaptive approaches and reliability estimations in finite element analysis. Zbl 0396.73077Babuška, Ivo; Rheinboldt, W. C. 35 1979 The problem of selecting the shape functions for a p-type finite element. Zbl 0705.73246Babuška, I.; Griebel, M.; Pitkäranta, J. 34 1989 The p-version of the finite element method for domains with corners and for infinite domains. Zbl 0717.65084Babuška, Ivo; Oh, Hae-Soo 33 1990 The h-p version of the finite element method for parabolic equations. I: The p-version in time. Zbl 0693.65078Babuška, Ivo; Janik, Tadeusz 33 1989 Regularity of the solutions for elliptic problems on nonsmooth domains in \(\mathbb{R}^ 3\). I: Countably normed spaces on polyhedral domains. Zbl 0874.35019Guo, Benqi; Babuška, Ivo 31 1997 Verification and validation in computational engineering and science: basic concepts. Zbl 1198.74126Babuska, Ivo; Oden, J. Tinsley 30 2004 The optimal symmetrical points for polynomial interpolation of real functions in the tetrahedron. Zbl 0877.65004Chen, Qi; Babuška, Ivo 30 1996 The problem of plate modeling: Theoretical and computational results. Zbl 0764.73040Babuška, I.; Li, Likang 30 1992 Introduction to finite element analysis. Formulation, verification and validation. Zbl 1410.65003Szabó, Barna; Babuška, Ivo 29 2011 A posteriori error estimation for finite element solutions of Helmholtz’ equation. I: The quality of local indicators and estimators. Zbl 0974.76042Babuška, I.; Ihlenburg, F.; Strouboulis, T.; Gangaraj, S. K. 29 1997 Analysis of the efficiency of an a posteriori error estimator for linear triangular finite elements. Zbl 0759.65069Babuška, Ivo; Durán, Ricardo; Rodríguez, Rodolfo 29 1992 Asymptotically exact a posteriori error estimator for biquadratic elements. Zbl 0619.73080Babuška, Ivo; Yu, Dehao 29 1987 \(p\)-version of the generalized FEM using mesh-based handbooks with applications to multiscale problems. Zbl 1059.65106Strouboulis, Theofanis; Zhang, Lin; Babuška, Ivo 28 2004 Locking effects in the finite element approximation of plate models. Zbl 0827.73063Suri, Manil; Babuška, Ivo; Schwab, Christoph 28 1995 A finite element scheme for domains with corners. Zbl 0252.65084Babuška, Ivo; Rosenzweig, Michael B. 28 1972 On roundoff error growth in elliptic problems. Zbl 07003058Babuška, Ivo; Söderlind, Gustaf 2 2018 Stable generalized finite element method and associated iterative schemes; application to interface problems. Zbl 1425.74472Kergrene, Kenan; Babuška, Ivo; Banerjee, Uday 12 2016 A fuzzy-stochastic multiscale model for fiber composites, a one-dimensional study. Zbl 1425.74126Babuška, Ivo; Motamed, Mohammad 3 2016 Bayesian inference and model comparison for metallic fatigue data. Zbl 1426.62295Babuška, Ivo; Sawlan, Zaid; Scavino, Marco; Szabó, Barna; Tempone, Raúl 2 2016 Stable GFEM (SGFEM): improved conditioning and accuracy of GFEM/XFEM for three-dimensional fracture mechanics. Zbl 1423.74886Gupta, V.; Duarte, C. A.; Babuška, I.; Banerjee, U. 22 2015 Higher order stable generalized finite element method. Zbl 1304.65254Zhang, Qinghui; Banerjee, Uday; Babuška, Ivo 12 2014 Machine computation using the exponentially convergent multiscale spectral generalized finite element method. Zbl 1320.74097Babuška, Ivo; Huang, Xu; Lipton, Robert 11 2014 A stochastic multiscale method for the elastodynamic wave equation arising from fiber composites. Zbl 1423.74966Babuška, Ivo; Motamed, Mohammad; Tempone, Raúl 7 2014 Dealing with uncertainties in engineering problems using only available data. Zbl 1296.76105Babuška, Ivo; Silva, Renato S. 1 2014 A stable and optimally convergent generalized FEM (SGFEM) for linear elastic fracture mechanics. Zbl 1286.74102Gupta, V.; Duarte, C. A.; Babuška, I.; Banerjee, U. 27 2013 Direct and inverse approximation theorems for the \(p\)-version of the finite element method in the framework of weighted Besov spaces. III: Inverse approximation theorems. Zbl 1382.65399Guo, Benqi; Babuška, Ivo 2 2013 Stable generalized finite element method (SGFEM). Zbl 1239.74093Babuška, I.; Banerjee, U. 77 2012 The dome and the ring: verification of an old mathematical model for the design of a stiffened shell roof. Zbl 1252.74043Pitkäranta, Juhani; Babuška, Ivo; Szabó, Barna 2 2012 Optimal local approximation spaces for generalized finite element methods with application to multiscale problems. Zbl 1229.65195Babuska, Ivo; Lipton, Robert 53 2011 Introduction to finite element analysis. Formulation, verification and validation. Zbl 1410.65003Szabó, Barna; Babuška, Ivo 29 2011 \(L^{2}\)-global to local projection: An approach to multiscale analysis. Zbl 1242.65234Babuska, Ivo; Lipton, Robert 10 2011 Finite elements. An introduction to the method and error estimation. Zbl 1206.65246Babuška, Ivo; Whiteman, John R.; Strouboulis, Theofanis 10 2011 The effect of numerical integration on the finite element approximation of linear functionals. Zbl 1210.65188Babuška, Ivo; Banerjee, Uday; Li, Hengguang 5 2011 Numerical treatment of engineering problems with uncertainties. The fuzzy set approach and its application to the heat exchanger problem. Zbl 1242.76228Babuška, Ivo; Silva, Renato S. 2 2011 A stochastic collocation method for elliptic partial differential equations with random input data. Zbl 1226.65004Babuška, Ivo; Nobile, Fabio; Tempone, Raúl 107 2010 A residual-based a posteriori error estimator for the Stokes-Darcy coupled problem. Zbl 1410.76148Babuška, Ivo; Gatica, Gabriel N. 41 2010 Local Jacobi operators and applications to the \(p\)-version of finite element method in two dimensions. Zbl 1218.65129Guo, Benqi; Babuška, Ivo 8 2010 \(n\)-widths, sup-infs, and optimality ratios for the \(k\)-version of the isogeometric finite element method. Zbl 1227.65093Evans, John A.; Bazilevs, Yuri; Babuška, Ivo; Hughes, Thomas J. R. 119 2009 Effect of numerical integration on meshless methods. Zbl 1229.65204Babuška, Ivo; Banerjee, Uday; Osborn, John E.; Zhang, Qinghui 23 2009 The generalized finite element method for Helmholtz equation. II: Effect of choice of handbook functions, error due to absorbing boundary conditions and its assessment. Zbl 1169.76397Strouboulis, Theofanis; Hidajat, Realino; Babuška, Ivo 25 2008 A systematic approach to model validation based on Bayesian updates and prediction related rejection criteria. Zbl 1139.74012Babuška, I.; Nobile, F.; Tempone, R. 21 2008 Quadrature for meshless methods. Zbl 1195.65165Babuška, Ivo; Banerjee, Uday; Osborn, John E.; Li, Qiaoluan 20 2008 Validation challenge workshop. Zbl 1155.74054Hills, Richard G.; Pilch, Martin; Dowding, Kevin J.; Red-Horse, John; Paez, Thomas L.; Babuška, Ivo; Tempone, Raul 14 2008 Generalized finite element method for second-order elliptic operators with Dirichlet boundary conditions. Zbl 1153.65106Babuška, Ivo; Nistor, Victor; Tarfulea, Nicolae 13 2008 Formulation of the static frame problem. Zbl 1388.74115Babuška, I. (ed.); Nobile, F. (ed.); Tempone, R. (ed.) 8 2008 Boundary value problems in spaces of distributions on smooth and polygonal domains. Zbl 1154.65085Babuška, Ivo; Nistor, Victor 6 2008 The penetration function and its application to microscale problems. Zbl 1152.65105Babuška, Ivo; Lipton, Robert; Stuebner, Michael 5 2008 Static frame challenge problem: Summary. Zbl 1140.74008Babuška, I.; Tempone, R. 2 2008 Validation challenge workshop summary. Zbl 1388.00029Dowding, Kevin J. (ed.); Red-Horse, John R. (ed.); Paez, Thomas L. (ed.); Babuška, Ivo M. (ed.); Hills, Richard G. (ed.); Tempone, Raul (ed.) 1 2008 A stochastic collocation method for elliptic partial differential equations with random input data. Zbl 1151.65008Babuška, Ivo; Nobile, Fabio; Tempone, Raúl 323 2007 Superconvergence in the generalized finite element method. Zbl 1129.65075Babuška, Ivo; Banerjee, Uday; Osborn, John E. 15 2007 Reliability of computational science. Zbl 1118.65030Babuška, I.; Nobile, F.; Tempone, R. 11 2007 Assessment of the cost and accuracy of the generalized FEM. Zbl 1194.74474Strouboulis, Theofanis; Zhang, Lin; Babuška, Ivo 8 2007 A global-local approach for the construction of enrichment functions for the generalized FEM and its application to three-dimensional cracks. Zbl 1323.74081Duarte, C. Armando; Kim, Dae-Jin; Babuška, Ivo 7 2007 Mechanics of materials with periodic truss or frame micro-structures. Zbl 1140.74532Martinsson, Per-Gunnar; Babuška, Ivo 7 2007 Homogenization of materials with periodic truss or frame micro-structures. Zbl 1115.74040Martinsson, P. G.; Babuška, Ivo 6 2007 Dynamic data-driven finite element models for laser treatment of cancer. Zbl 1114.92043Oden, J. T.; Diller, K. R.; Bajaj, C.; Browne, J. C.; Hazle, J.; Babuška, I.; Bass, J.; Biduat, L.; Demkowicz, L.; Elliott, A.; Feng, Y.; Fuentes, D.; Prudhomme, S.; Rylander, M. N.; Stafford, R. J.; Zhang, Y. 4 2007 Approximate and low regularity Dirichlet boundary conditions in the generalized finite element method. Zbl 1145.65093Babuška, Ivo; Nistor, Victor; Tarfulea, Nicolae 3 2007 Interior maximum norm estimates for finite element discretizations of the Stokes equations. Zbl 1122.65101Narasimhan, R.; Babuška, I. 3 2007 The generalized finite element method for Helmholtz equation: theory, computation, and open problems. Zbl 1120.76044Strouboulis, Theofanis; Babuška, Ivo; Hidajat, Realino 59 2006 A posteriori error estimation for generalized finite element methods. Zbl 1119.65111Strouboulis, Theofanis; Zhang, Lin; Wang, Delin; Babuška, Ivo 24 2006 Interior numerical approximation of boundary value problems with a distributional data. Zbl 1101.65105Babuška, Ivo; Nistor, Victor 7 2006 On the generalized plane strain problem in thermoelasticity. Zbl 1124.74011Babuška, Ivo; Szabó, Barna 2 2006 The reliability of computer predictions: can they be trusted? Zbl 1096.65043Babuška, Ivo; Oden, J. Tinsley 2 2006 Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation. Zbl 1087.65004Babuška, Ivo; Tempone, Raúl; Zouraris, Georgios E. 101 2005 Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty. Zbl 1143.74373Oden, J. Tinsley; Babuška, Ivo; Nobile, Fabio; Feng, Yusheng; Tempone, Raul 17 2005 Worst case scenario analysis for elliptic problems with uncertainty. Zbl 1082.65115Babuška, I.; Nobile, F.; Tempone, R. 15 2005 The splitting method as a tool for multiple damage analysis. Zbl 1149.65321Babuska, Ivo; Andersson, Börje 3 2005 New fictitious domain methods: formulation and analysis. Zbl 1107.65102Babuška, Ivo; Podnos, Eugene G.; Rodin, Gregory J. 1 2005 Galerkin finite element approximations of stochastic elliptic partial differential equations. Zbl 1080.65003Babuska, Ivo; Tempone, Raúl; Zouraris, Georgios E. 303 2004 Generalized finite element methods – main ideas, results and perspective. Zbl 1081.65107Babuška, Ivo; Banerjee, Uday; Osborn, John E. 60 2004 Verification and validation in computational engineering and science: basic concepts. Zbl 1198.74126Babuska, Ivo; Oden, J. Tinsley 30 2004 \(p\)-version of the generalized FEM using mesh-based handbooks with applications to multiscale problems. Zbl 1059.65106Strouboulis, Theofanis; Zhang, Lin; Babuška, Ivo 28 2004 On the approximability and the selection of particle shape functions. Zbl 1054.65116Babuška, Ivo; Banerjee, Uday; Osborn, John E. 14 2004 Uncertain input data problems and the worst scenario method. Zbl 1116.74003Hlaváček, Ivan; Chleboun, Jan; Babuška, Ivo 12 2004 Algebraic algorithms for the analysis of mechanical trusses. Zbl 1079.74045Babuška, I.; Sauter, S. A. 3 2004 Efficient solution of lattice equations by the recovery method. I: Scalar elliptic problems. Zbl 1076.65097Babuška, I.; Sauter, S. A. 1 2004 Survey of meshless and generalized finite element methods: A unified approach. Zbl 1048.65105Babuška, Ivo; Banerjee, Uday; Osborn, John E. 132 2003 Generalized finite element method using mesh-based handbooks: application to problems in domains with many voids. Zbl 1054.74059Strouboulis, Theofanis; Zhang, Lin; Babuška, Ivo 47 2003 \(p\) interpolation error estimates for edge finite elements of variable order in two dimensions. Zbl 1067.78016Demkowicz, L.; Babuska, I. 27 2003 On the mixed finite element method with Lagrange multipliers. Zbl 1021.65056Babuška, Ivo; Gatica, Gabriel N. 24 2003 Research directions in computational mechanics. Zbl 1025.74503Oden, J. Tinsley; Belytschko, Ted; Babuska, Ivo; Hughes, T. J. R. 22 2003 Solving stochastic partial differential equations based on the experimental data. Zbl 1052.60047Babuška, Ivo; Liu, Kang-Man; Tempone, Raúl 18 2003 Effects of uncertainties in the domain on the solution of Dirichlet boundary value problems. Zbl 1016.65088Babuška, Ivo; Chleboun, Jan 11 2003 On solving stochastic initial-value differential equations. Zbl 1049.60051Babuška, Ivo; Liu, Kang-Man 7 2003 Guaranteed a posteriori error estimation for fully discrete solutions of parabolic problems. Zbl 1025.65052Strouboulis, T.; Babuška, I.; Datta, D. K. 5 2003 On solving elliptic stochastic partial differential equations. Zbl 1019.65010Babuška, Ivo; Chatzipantelidis, Panagiotis 65 2002 Meshless and generalized finite element methods: A survey of some major results. Zbl 1012.65119Babuška, I.; Banerjee, U.; Osborn, J. E. 26 2002 On principles for the selection of shape functions for the generalized finite element method. Zbl 1016.65052Babuška, Ivo; Banerjee, Uday; Osborn, John E. 17 2002 Effects of uncertainties in the domain on the solution of Neumann boundary value problems in two spatial dimensions. Zbl 1007.65086Babuška, Ivo; Chleboun, Jan 15 2002 Mesh-independent \(p\)-orthotropic enrichment using the generalized finite element method. Zbl 1027.74065Duarte, C. A.; Babuška, I. 13 2002 Direct and inverse approximation theorems for the \(p\)-version of the finite element method in the framework of weighted Besov spaces. II: Optimal rate of convergence of the \(p\)-version finite element solutions. Zbl 1026.65103Babuška, Ivo; Guo, Benqi 11 2002 Can we trust the computational analysis of engineering problems? Zbl 1004.65059Babuška, I.; Strouboulis, T. 4 2002 Mathematical modeling and numerical simulation in continuum mechanics. Proceedings of the international symposium, Yamaguchi, Japan, September 29 – October 3, 2000. Zbl 0976.00035Babuška, Ivo (ed.); Ciarlet, Philippe G. (ed.); Miyoshi, Tetsuhiko (ed.) 1 2002 The generalized finite element method. Zbl 0997.74069Strouboulis, T.; Copps, K.; Babuška, I. 300 2001 The finite element methods and its reliability. Zbl 0995.65501Babuška, Ivo; Strouboulis, Theofanis 146 2001 Solution of stochastic partial differential equations using Galerkin finite element techniques. Zbl 1075.65006Deb, Manas K.; Babuška, Ivo M.; Oden, J. Tinsley 143 2001 Direct and inverse approximation theorems for the \(p\)-version of the finite element method in the framework of weighted Besov spaces. I: Approximability of functions in the weighted Besov spaces. Zbl 1008.65078Babuška, Ivo; Guo, Benqi 38 2001 A posteriori error estimation for the semidiscrete finite element method of parabolic differential equations. Zbl 1013.65099Babuška, I.; Ohnimus, S. 15 2001 On one approach to a posteriori error estimates for evolution problems solved by the method of lines. Zbl 0993.65103Babuška, Ivo; Feistauer, Miloslav; Šolín, Pavel 11 2001 A posteriori estimators for the FEM: Analysis of the robustness of the estimators for the Poisson equation. Zbl 0991.65110Zhang, L.; Strouboulis, T.; Babuška, I. 2 2001 \(\eta\)%-superconvergence of finite element solutions and error estimators. Zbl 0991.65109Zhang, L.; Strouboulis, T.; Babuška, I. 1 2001 The design and analysis of the generalized finite element method. Zbl 0983.65127Strouboulis, T.; Babuška, I.; Copps, K. 238 2000 The generalized finite element method: An example of its implementation and illustration of its performance. Zbl 0955.65080Strouboulis, T.; Copps, K.; Babuška, I. 98 2000 Is the pollution effect of the FEM avoidable for the Helmholtz equation considering high wave numbers? Zbl 0956.65095Babuska, Ivo M.; Sauter, Stefan A. 92 2000 Can a finite element method perform arbitrarily badly? Zbl 0940.65086Babuska, Ivo; Osborn, John E. 40 2000 A posteriori estimation and adaptive control of the error in the quantity of interest. I: A posteriori estimation of the error in the von Mises stress and the stress intensity factor. Zbl 0973.74083Strouboulis, T.; Babuška, I.; Datta, D. K.; Copps, K.; Gangaraj, S. K. 27 2000 Generalized \(p\)-FEM in homogenization. Zbl 0964.65125Matache, Ana-Maria; Babuška, Ivo; Schwab, Christoph 21 2000 Optimal estimates for lower and upper bounds of approximation errors in the \(p\)-version of the finite element method in two dimensions. Zbl 0970.65117Babuška, Ivo; Guo, Benqi 19 2000 Guaranteed computable bounds for the exact error in the finite element solution. II: Bounds for the energy norm of the error in two dimensions. Zbl 0962.65069Strouboulis, T.; Babuška, I.; Gangaraj, S. K. 14 2000 What do we want and what do we have in a posteriori estimates in the FEM. Zbl 0960.65119Babuška, Ivo; Strouboulis, Theofanis; Datta, Dibyendu; Gangaraj, Srihari 1 2000 Dispersion and pollution of the FEM solution for the Helmholtz equation in one, two and three dimensions. Zbl 0957.65098Deraemaeker, Arnaud; Babuška, Ivo; Bouillard, Philippe 95 1999 Damage analysis of fiber composites. I: Statistical analysis of fiber scale. Zbl 0956.74048Babuška, Ivo; Andersson, Börje; Smith, Paul J.; Levin, Klas 62 1999 A discontinuous \(hp\) finite element method for diffusion problems: 1-D analysis. Zbl 0940.65076Babuška, I.; Baumann, C. E.; Oden, J. T. 45 1999 A posteriori error estimation for the finite element method-of-lines solution of parabolic problems. Zbl 0937.65101Adjerid, Slimane; Flaherty, Joseph E.; Babuška, Ivo 24 1999 ...and 219 more Documents all cited Publications top 5 cited Publications all top 5 Cited by 8,684 Authors 144 Babuška, Ivo 67 Oden, John Tinsley 61 Schwab, Christoph 52 Hughes, Thomas J. R. 51 Demkowicz, Leszek F. 50 Zhang, Zhimin 42 Rank, Ernst 37 Bordas, Stéphane Pierre Alain 37 Ladevèze, Pierre 37 Yang, Yidu 36 Carstensen, Carsten 36 Düster, Alexander 35 Belytschko, Ted Bohdan 33 Tempone, Raúl F. 31 Nobile, Fabio 30 Ainsworth, Mark 30 Xie, Hehu 29 Repin, Sergeĭ Igorevich 29 Stephan, Ernst Peter 29 Wheeler, Mary Fanett 28 Gatica, Gabriel N. 28 Strouboulis, Theofanis 28 Zheng, Hong 27 Huang, Yunqing 27 Karniadakis, George Em 27 Nicaise, Serge 27 Rabczuk, Timon 26 Bazilevs, Yuri 26 Bi, Hai 26 Díez, Pedro 26 Huerta, Antonio 25 Flaherty, Joseph E. 25 Lin, Tao 25 Moës, Nicolas 25 Quarteroni, Alfio M. 25 Sangalli, Giancarlo 25 Trevelyan, Jon 24 Brenner, Susanne Cecelia 24 Chen, Yanping 24 Gunzburger, Max D. 24 Li, Zi-Cai 24 Suri, Manil 23 Beirão da Veiga, Lourenço 23 Calo, Victor Manuel 23 Duarte, C. A. 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