Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading

DOI10.1016/j.apnum.2011.06.015zbMath1253.65184OpenAlexW2049119935MaRDI QIDQ412308

Alexey Chernov

Publication date: 4 May 2012

Published in: Applied Numerical Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.apnum.2011.06.015

zbMATH Keywords

Sobolev spacesfinite element methodspectral element methodnumerical exampleselliptic differential equationoptimal convergencecontinuous finite elements\(p\)-version FEMelliptic integral equationrandom datasparse polynomial discretizationsparse tensor product polynomials

Mathematics Subject Classification ID

Numerical methods for integral equations (65R20) Boundary value problems for second-order elliptic equations (35J25) Integro-partial differential equations (45K05) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items (7)

New explicit-in-dimension estimates for the cardinality of high-dimensional hyperbolic crosses and approximation of functions having mixed smoothness ⋮ A multilevel sparse kernel-based stochastic collocation finite element method for elliptic problems with random coefficients ⋮ \(N\)-widths and \(\varepsilon \)-dimensions for high-dimensional approximations ⋮ Sparse tensor product spectral Galerkin BEM for elliptic problems with random input data on a spheroid ⋮ On \(n\)-widths of a Sobolev function class in Orlicz spaces ⋮ Adjusted sparse tensor product spectral Galerkin method for solving pseudodifferential equations on the sphere with random input data ⋮ Tensor train approximation of moment equations for elliptic equations with lognormal coefficient

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Sparse \(p\)-version BEM for first kind boundary integral equations with random loading
• Sparse second moment analysis for elliptic problems in stochastic domains
• Sparse finite element methods for operator equations with stochastic data.
• A finite element method for elliptic problems with stochastic input data
• A finite element method for some integral equations of the first kind
• Sparse finite elements for stochastic elliptic problems --- higher order moments
• Sparse finite elements for elliptic problems with stochastic loading
• Sparse grids for boundary integral equations
• An introduction to infinite-dimensional analysis
• Karhunen-Loève approximation of random fields by generalized fast multipole methods
• hp-FEM for second moments of elliptic PDEs with stochastic data. II: Exponential convergence for stationary singular covariance functions
• Numerical Approximation Methods for Elliptic Boundary Value Problems
• Convergence rates for sparse chaos approximations of elliptic problems with stochastic coefficients
• A Sparse Grid Stochastic Collocation Method for Partial Differential Equations with Random Input Data
• The $h-p$ version of the finite element method with quasiuniform meshes
• The Optimal Convergence Rate of the p-Version of the Finite Element Method
• A Posteriori Error Estimates for Boundary Element Methods
• Sparse grids
• Equivalent Norms for Sobolev Spaces
• On randomised solutions of Laplace's equation
• Solution of stochastic partial differential equations using Galerkin finite element techniques

This page was built for publication: Sparse polynomial approximation in positive order Sobolev spaces with bounded mixed derivatives and applications to elliptic problems with random loading