Adaptive Galerkin finite element methods for partial differential equations
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. VII: partial differential equations
hp-Adaptive Discontinuous Galerkin Finite Element Methods for First-Order Hyperbolic Problems
SIAM Journal on Scientific Computing
Finite Elements in Analysis and Design
An Adjoint-Based A Posteriori Estimation of Iterative Convergence Error
Computers & Mathematics with Applications
Estimation of goal functional error arising from iterative solution of Euler equations
International Journal of Computational Fluid Dynamics
Adjoint correction and bounding of error using lagrange form of truncation term
Computers & Mathematics with Applications
A posteriori error estimation by postprocessor independent of method of flowfield calculation
Computers & Mathematics with Applications
Finite Elements in Analysis and Design
A computational infrastructure for reliable computer simulations
ICCS'03 Proceedings of the 2003 international conference on Computational science
Predicting goal error evolution from near-initial-information: A learning algorithm
Journal of Computational Physics
Estimating the effects of removing negative features on engineering analysis
Computer-Aided Design
Estimating defeaturing-induced engineering analysis errors for arbitrary 3D features
Computer-Aided Design
ICCS'05 Proceedings of the 5th international conference on Computational Science - Volume Part I
Quantitative control of idealized analysis models of thin designs
Computers and Structures
A generalized adaptive finite element analysis of laminated plates
Computers and Structures
Multiphysics simulations: Challenges and opportunities
International Journal of High Performance Computing Applications
Estimation of computational homogenization error by explicit residual method
Computers & Mathematics with Applications
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We review and extend the theory and methodology of a posteriori error estimation and adaptivity for modeling error for certain classes of problems in linear and nonlinear mechanics. The basic idea is that for a given collection of physical phenomena a rich class of mathematical models can be identified, including models that are sufficiently refined and validated that they satisfactorily capture the events of interest. These fine models may be intractable, too complex to solve by existing means. Coarser models are therefore used. Moreover, as is frequently the case in applications, there are specific quantities of interest that are sought which are functionals of the solution of the fine model. In this paper, techniques for estimating modeling errors in such quantities of interest are developed. Applications to solid and fluid mechanics are presented.