Numerical Approximation of Optimal Convergence for Fractional Elliptic Equations with Additive Fractional Gaussian Noise

DOI10.1137/20M1374286zbMath1503.65304OpenAlexW3184844169MaRDI QIDQ5010088

Zhongqiang Zhang, Zhao-peng Hao

Publication date: 24 August 2021

Published in: SIAM/ASA Journal on Uncertainty Quantification (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1137/20m1374286

zbMATH Keywords

regularityfractional Gaussian noisespectral Galerkin methodsintegral fractional Laplacianpink noiseultraweak Petrov-Galerkin

Mathematics Subject Classification ID

Fractional processes, including fractional Brownian motion (60G22) Smoothness and regularity of solutions to PDEs (35B65) Spectral, collocation and related methods for boundary value problems involving PDEs (65N35) Brownian motion (60J65) Fractional derivatives and integrals (26A33) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs (65M70) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Rate of convergence, degree of approximation (41A25) Fractional partial differential equations (35R11) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Regularization by noise (60H50)

Related Items (3)

Optimal error estimates of spectral Galerkin method for mixed diffusion equations ⋮ On spectral Petrov-Galerkin method for solving optimal control problem governed by fractional diffusion equations with fractional noise ⋮ Optimal strong convergence of finite element methods for one-dimensional stochastic elliptic equations with fractional noise

Uses Software

• cnoise

Cites Work

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