Efficient Distribution Estimation and Uncertainty Quantification for\n Elliptic Problems on Domains with Stochastic Boundaries

2018/07/13 by Jehanzeb H. Chaudhry, Chaudhry, Jehanzeb H, Nathanial Burch +3 · 1 citation
Decision Sciences · Engineering · Mathematics · #FOS: Mathematics #Numerical Analysis (math.NA) #Probabilistic and Robust Engineering Design #Reservoir Engineering and Simulation Methods #Statistical Methods and Inference

paper · pdf · doi:10.48550/arxiv.1807.05296

openalex publication_date 2018/07/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the problem of uncertainty quantification for the numerical solution\nof elliptic partial differential equation boundary value problems posed on\ndomains with stochastically varying boundaries. We also use the uncertainty\nquantification results to tackle the efficient solution of such problems. We\nintroduce simple transformations that map a family of domains with stochastic\nboundaries to a fixed reference domain. We exploit the transformations to carry\nout a prior and a posteriori error analyses and to derive an efficient Monte\nCarlo sampling procedure.\n

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