• I. Babuska, F. Nobile and R. Tempone. ”Worst-case scenario analysis for elliptic PDE’s with uncertainty”, Proceedings of the EURODYN conference, Paris, September 4-7, 2005.​

Keywords: Worst-case scenario analysis for elliptic PDE’s with uncertainty

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  • Oden, J. Tinsley; Babuška, Ivo; Nobile, Fabio; Feng, Yusheng; Tempone, Raul "Theory and methodology for estimation and control of errors due to modeling, approximation, and uncertainty." Comput. Methods Appl. Mech. Engrg. 194 (2005), no. 2-5, 195–204.​

Keywords: Modeling error estimation; Stochastic partial differential equations; Adaptive modeling.

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  • Babuška, Ivo; Tempone, Raúl; Zouraris, Georgios E. "Solving elliptic boundary value problems with uncertain coefficients by the finite element method: the stochastic formulation." Comput. Methods Appl. Mech. Engrg. 194 (2005), no. 12-16, 1251–1294.​

Keywords: Stochastic elliptic equation; Perturbation estimates; Karhunen–Loève expansion; Finite elements; Monte Carlo method, k × h-version; p × h-version; Expected value; Error estimates; Adaptive methods; Error control.

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  • Moon, Kyoung-Sook; Szepessy, Anders; Tempone, Raúl; Zouraris, Georgios E. "Convergence rates for the adaptive weak approximation of stochastic differential equations." Stoch. Anal. Appl. 23 (2005), no. 3, 511–558.​

Keywords: Adaptive mesh refinement algorithm, Almost sure convergence, Computational complexity, Monte Carlo method, Stochastic differential equations.

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  • Dzougoutov, Anna; Moon, Kyoung-Sook; von Schwerin, Erik; Szepessy, Anders; Tempone, Raúl "Adaptive Monte Carlo algorithms for stopped diffusion." Multiscale methods in science and engineering, 59–88, Lect. Notes Comput. Sci. Eng., 44, Springer, Berlin, 2005.​

Keywords: adaptive mesh refinement, algorithm, diffusion with boundary, barrier option, Monte Carlo method, weak approximation.

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  • Babuška, I.; Nobile, F.; Tempone, R. "Worst case scenario analysis for elliptic problems with uncertainty", Numerische Mathematik, Volume 101, Issue 2, pp 185-219, August 2005.

Keywords: Worst case scenario analysis for elliptic problems with uncertainty

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  • Moon, Kyoung-Sook; von Schwerin, Erik; Szepessy, Anders; Tempone, Raúl  "An adaptive algorithm for ordinary, stochastic and partial differential equations." Recent advances in adaptive computation, 325–343, Contemp. Math., 383, Amer. Math. Soc., Providence, RI, 2005.​

Keywords: adaptive methods, mesh refinement algorithm, a posteriori error estimate, computational complexity.

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