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- Donald J. Estep, Victor Ginting, David L. Ropp, John N. Shadid, Simon Tavener
- SIAM J. Numerical Analysis
- 2008

In this paper, we analyze a multiscale operator splitting method for solving systems of ordinary differential equations such as those that result upon space discretization of a reaction-diffusion equation. Our goal is to analyze and accurately estimate the error of the numerical solution, including the effects of any instabilities that can result from… (More)

- Donald J. Estep, Simon Tavener, Tim Wildey
- SIAM J. Numerical Analysis
- 2008

We consider the accuracy of an operator decomposition finite element method for a conjugate heat transfer problem consisting of two materials coupled through a common boundary. We derive accurate a posteriori error estimates that account for the transfer of error between components of the operator decomposition method as well as the differences between the… (More)

- Donald J. Estep, Simon Tavener, Tim Wildey
- J. Comput. Physics
- 2010

Keywords: Adjoint problem Adaptive mesh refinement A posteriori error analysis Boundary flux correction Conjugate heat transfer Finite element method Flux recovery Greens functions Operator decomposition Multi-discretization methods Multiscale methods a b s t r a c t We analyze a multiscale operator decomposition finite element method for a conjugate heat… (More)

- Donald J. Estep, Axel Målqvist, Simon Tavener
- SIAM J. Scientific Computing
- 2009

We consider the nonparametric density estimation problem for a quantity of interest computed from solutions of an elliptic partial differential equation with randomly perturbed coefficients and data. Our particular interest are problems for which limited knowledge of the random perturbations are known. We derive an efficient method for computing samples and… (More)

- Varis Carey, Donald J. Estep, Simon Tavener
- SIAM J. Numerical Analysis
- 2008

In this paper, we perform an a posteriori error analysis of a multiscale operator decomposition finite element method for the solution of a system of coupled elliptic problems. The goal is to compute accurate error estimates that account for the effects arising from multiscale discretization via operator decomposition. Our approach to error estimation is… (More)

- T. Wildey, S. Tavener, D. Estep
- 2006

SUMMARY This paper describes the a posteriori estimation of the error in the flux of a finite element approximation on a piece of the boundary of the domain. The estimate is obtained via a generalized Green's function corresponding to the quantity of interest on the boundary. We investigate the effects of smoothing the data corresponding to the quantity of… (More)

- Donald J. Estep, Michael Pernice, Du Pham, Simon Tavener, Haiying Wang
- J. Computational Applied Mathematics
- 2009

In this paper, we conduct an a posteriori analysis for the error in a quantity of interest computed from a cell-centered finite volume scheme. The a posteriori error analysis is based on variational analysis, residual error and the adjoint problem. To carry out the analysis, we use an equivalence between the cell-centered finite volume scheme and a mixed… (More)

- D C Apperley, R A Fletton, R K Harris, R W Lancaster, S Tavener, T L Threlfall
- Journal of pharmaceutical sciences
- 1999

The literature on sulfathiazole polymorphs has many confusions and inconsistencies. These are largely resolved by the distinctive appearance of (13)C magic-angle spinning NMR spectra, which immediately show the number of molecules in the crystallographic asymmetric unit. The spectra presented include those of a newly-recognized form. The assignments of the… (More)

- D. Estep, A. Målqvist, S. Tavener
- 2008

SUMMARY In this paper, we develop and apply an efficient adaptive algorithm for computing the propagation of uncertainty into a quantity of interest computed from numerical solutions of an elliptic partial differential equation with a randomly perturbed diffusion coefficient. The algorithm is well-suited for problems for which limited information about the… (More)

- Lorenz Berger, Rafel Bordas, David Kay, Simon Tavener
- SIAM J. Scientific Computing
- 2015

A stabilized conforming finite element method for the three-field (displacement, fluid flux and pressure) poroelasticity problem is presented. We use the lowest possible approximation order: piecewise constant approximation for the pressure, and piecewise linear continuous elements for the displacements and fluid flux. By applying a local pressure jump… (More)