Multilevel Monte Carlo method with applications to stochastic partial differential equations

DOI10.1080/00207160.2012.701735zbMath1270.65003OpenAlexW2060386985MaRDI QIDQ4902859

Andrea Barth, Annika Lang

Publication date: 18 January 2013

Published in: International Journal of Computer Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00207160.2012.701735

zbMATH Keywords

heat equationnumerical examplesstochastic partial differential equationmultilevel approximationstochastic parabolic equationmultilevel Monte Carlo methodstochastic finite element methodsfirst-order hyperbolic equationlinearized backward Euler scheme

Mathematics Subject Classification ID

Random fields (60G60) Monte Carlo methods (65C05) Heat equation (35K05) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) PDEs with randomness, stochastic partial differential equations (35R60) Computational methods for stochastic equations (aspects of stochastic analysis) (60H35) Numerical solutions to stochastic differential and integral equations (65C30) First-order hyperbolic equations (35L02)

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Cites Work

• Multilevel Monte Carlo methods and applications to elliptic PDEs with random coefficients
• A multilevel Monte Carlo algorithm for Lévy-driven stochastic differential equations
• The exponential integrator scheme for stochastic partial differential equations: Pathwise error bounds
• Multi-level Monte Carlo finite element method for elliptic PDEs with stochastic coefficients
• Stability of the SUPG finite element method for transient advection-diffusion problems
• Weak convergence of finite element approximations of linear stochastic evolution equations with additive noise
• Semigroups of linear operators and applications to partial differential equations
• Multilevel Monte Carlo Path Simulation
• The Multilevel Monte Carlo method used on a Lévy driven SDE
• Stochastic Partial Differential Equations with Levy Noise

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