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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 reactiondiffusion… (More)

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

Abstract. 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… (More)

- Donald J. Estep, Andrew M. Stuart
- Math. Comput.
- 2002

We study the dynamical behavior of the discontinuous Galerkin finite element method for initial value problems in ordinary differential equations. We make two different assumptions which guarantee… (More)

We consider the problem of estimating the p-quantile for a given functional evaluated on solutions of a deterministic model in which model input is subject to stochastic variation. We derive upper… (More)

A posteriori error analysis of a cell-centered finite volume method for semilinear elliptic problems

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

In this paper, we conduct a goal-oriented a posteriori analysis for the error in a quantity of interest computed from a cell-centered finite volume scheme for a semilinear elliptic problem. The a… (More)

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

Article history: Received 28 March 2008 Received in revised form 7 January 2010 Accepted 4 February 2010 Available online 17 February 2010

- Donald J. Estep, Michael J. Holst, Mats Larson
- SIAM J. Scientific Computing
- 2005

One well-known approach to a posteriori analysis of finite element solutions of elliptic problems estimates the error in a quantity of interest in terms of residuals and a generalized Green’s… (More)

- David E. Keyes, Lois C. McInnes, +42 authors Barbara I. Wohlmuth
- IJHPCA
- 2013

We consider multiphysics applications from algorithmic and architectural perspectives, where “algorithmic” includes both mathematical analysis and computational complexity and “architectural”… (More)

We describe a MIMD parallel code to solve a general class of ordinary di erential equations, with particular emphasis on the large, sparse systems arising from space discretization of systems of… (More)

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… (More)