Articlebronze2013

First order second moment analysis for stochastic interface problems based on low-rank approximation

45 citations0/0 files storedESAIM Mathematical Modelling and Numerical Analysis

No readable copy stored yet — this record is metadata only.

No open-access location is known for this record yet.

Literature note Cite in a project Citation map

Probabilistic and Robust Engineering Design Advanced Numerical Methods in Computational Mathematics Advanced Mathematical Modeling in Engineering

Abstract

In this paper, we propose a numerical method to solve stochastic elliptic interface problems with random interfaces. Shape calculus is first employed to derive the shape-Taylor expansion in the framework of the asymptotic perturbation approach. Given the mean field and the two-point correlation function of the random interface, we can thus quantify the mean field and the variance of the random solution in terms of certain orders of the perturbation amplitude by solving a deterministic elliptic interface problem and its tensorized counterpart with respect to the reference interface. Error estimates are derived for the interface-resolved finite element approximation in both, the physical and the stochastic dimension. In particular, a fast finite difference scheme is proposed to compute the variance of random solutions by using a low-rank approximation based on the pivoted Cholesky decomposition. Numerical experiments are presented to validate and quantify the method.

Paper brief

Loading…

Cite this work

Citation unavailable for this work.

BibTeX RIS CSL-JSON

No public copy is stored for this record, so only the metadata is cited.

Citations in this library

Citation map →

Stored only when both papers are in the corpus — 45 citations exist upstream.

References

1991Stochastic Finite Elements: A Spectral Approach 2016Numerical solution of stochastic differential equations 2007A Stochastic Collocation Method for Elliptic Partial Differential Equations with Random Input Data 2004Galerkin Finite Element Approximations of Stochastic Elliptic Partial Differential Equations 2014Stochastic Integration and Differential Equations : A New Approach 2004Galerkin methods for linear and nonlinear elliptic stochastic partial differential equations 2002Modeling uncertainty in steady state diffusion problems via generalized polynomial chaos 2004Numerical Challenges in the Use of Polynomial Chaos Representations for Stochastic Processes

Cited by

2016Uncertainty Quantification 2015Multi-level Monte Carlo weak Galerkin method for elliptic equations with stochastic jump coefficients 2021EMBEDDED MULTILEVEL MONTE CARLO FOR UNCERTAINTY QUANTIFICATION IN RANDOM DOMAINS 2016Numerical Solution of the Poisson Equation on Domains with a Thin Layer of Random Thickness 2020A domain mapping approach for elliptic equations posed on random bulk and surface domains

Explore the map →

Papers that cite the same references — the relational fallback while embeddings are still backfilling.

Imported from OpenAlex (CC0) — nothing here is generated.