Ivo Babuška

The University of Texas at Austin

Author Statistics

Papers

Citation

H-Index

i-10 index

Research Trends

Author Order

Document Type

Co-Authors

Barna Szabó

Washington University in St. Louis

T. Strouboulis

Texas A&M University

John E. Osborn

Southwestern University

Uday Banerjee

Syracuse University

Raúl Tempone

RWTH Aachen University

Manil Suri

University of Maryland, Baltimore County

S.K. Gangaraj

Texas A&M University

Werner C. Rheinboldt

University of Pittsburgh

Jan Chleboun

Czech Technical University in Prague

J. Tinsley Oden

Polytechnique Montréal

Cooperative Institutions

The University of Texas at Austin

University of Maryland, College Park

Sandia National Laboratories California

Washington University in St. Louis

Applied Mathematics (United States)

Sandia National Laboratories

Czech Academy of Sciences, Institute of Mathematics

Czech Academy of Sciences

Brunel University of London

University of Vermont

Author Statistics

Papers

Citation

H-Index

i-10 index

Research Field

Generalized finite element methods for three-dimensional structural mechanics problems

Computers & Structures (2000)

C. Armando Duarte Ivo Babuška J. Tinsley Oden

Orthotropic material

Elasticity

Structural Mechanics

Computational mechanics

10.1016/s0045-7949(99)00211-4

Cite

Citations (607)

A Posteriori Error Estimation for Hierarchic Models of Elliptic Boundary Value Problems on Thin Domains

SIAM Journal on Numerical Analysis (1996)

Ivo Babuška C. Schwab

The boundary value problem of heat conduction in a three-dimensional laminated plate is approximated by a hierarchy of two-dimensional models. Computable a posteriors indicators and estimators of the modeling error in various norms are derived and their local spectral and asymptotic exactness is proved. Sharp estimates for their effectivity indices are also obtained.

Value (mathematics)

10.1137/0733013

Cite

Citations (68)

Finite element method for solving problems with singular solutions

Journal of Computational and Applied Mathematics (1996)

Ivo Babuška B. Andersson Binghui Guo Jens Markus Melenk Hae‐Soo Oh

Partition of unity

10.1016/0377-0427(96)00017-9

Cite

Citations (36)

Adaptive procedure for approximating functions by continuous piecewise polynomials

Communications in Numerical Methods in Engineering (1996)

Qi Chen Ivo Babuška

The problem of approximating functions is considered in a general domain in one and two dimensions using piecewise polynomial interpolation. An error estimator is proposed which shows how to adaptively determine the interpolation degree. Numerical examples are given.

Interpolation

Degree (music)

10.1002/(sici)1099-0887(199608)12:8<483::aid-cnm996>3.0.co;2-x

Cite

Citations (3)

Finite Element Solution of the Helmholtz Equation with High Wave Number Part II: The h-p Version of the FEM

SIAM Journal on Numerical Analysis (1997)

Frank Ihlenburg Ivo Babuška

In this paper, which is part II in a series of two, the investigation of the Galerkin finite element solution to the Helmholtz equation is continued. While part I contained results on the h version with piecewise linear approximation, the present part deals with approximation spaces of order $p \ge 1$. As in part I, the results are presented on a one-dimensional model problem with Dirichlet--Robin boundary conditions. In particular, there are proven stability estimates, both with respect to data of higher regularity and data that is bounded in lower norms. The estimates are shown both for the continuous and the discrete spaces under consideration. Further, there is proven a result on the phase difference between the exact and the Galerkin finite element solutions for arbitrary p that had been previously conjectured from numerical experiments. These results and further preparatory statements are then employed to show error estimates for the Galerkin finite element method (FEM). It becomes evident that the error estimate for higher approximation can---with certain assumptions on the data---be written in the same form as the piecewise linear case, namely, as the sum of the error of best approximation plus a pollution term that is of the order of the phase difference. The paper is concluded with a numerical evaluation.

Helmholtz equation

Helmholtz free energy

10.1137/s0036142994272337

Cite

Citations (372)

K problematice teorie pružnosti

Časopis pro pěstování matematiky (1952)

Ivo Babuška

Source

Cite

Citations (0)

Direct and inverse error estimates for finite elements with mesh refinements