Combination Technique Based Second Moment Analysis for Elliptic PDEs on Random Domains

DOI10.1007/978-3-319-28262-6_3zbMath1339.65015OpenAlexW2475006845MaRDI QIDQ2808017

Helmut Harbrecht, Michael D. Multerer

Publication date: 26 May 2016

Published in: Lecture Notes in Computational Science and Engineering (Search for Journal in Brave)

Full work available at URL: http://edoc.unibas.ch/42291/1/20160323104650_56f2660a974f4.pdf

zbMATH Keywords

sparse gridGalerkin's methodnumerical experimentelliptic equationrandom domaintensor product Dirichlet problem

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) 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)

Related Items

The second order perturbation approach for elliptic partial differential equations on random domains, Hybrid three-scale model for evolving pore-scale geometries

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Combination technique based \(k\)-th moment analysis of elliptic problems with random diffusion
• Fast matrix-vector multiplication in the sparse-grid Galerkin method
• On finite element approximations of problems having inhomogeneous essential boundary conditions
• Sparse second moment analysis for elliptic problems in stochastic domains
• Multilevel frames for sparse tensor product spaces
• Sparse finite element methods for operator equations with stochastic data.
• A finite element method for elliptic problems with stochastic input data
• Sparse finite elements for stochastic elliptic problems --- higher order moments
• Sparse finite elements for elliptic problems with stochastic loading
• Error analysis of the combination technique
• A fictitious domain approach to the numerical solution of PDEs in stochastic domains
• Karhunen-Loève approximation of random fields by generalized fast multipole methods
• Stochastic analysis of transport in tubes with rough walls
• Fast Boolean approximation methods for solving integral equations in high dimensions
• Finite Element Based Second Moment Analysis for Elliptic Problems in Stochastic Domains
• Stochastic projection schemes for deterministic linear elliptic partial differential equations on random domains
• Numerical Methods for Differential Equations in Random Domains
• Parallel Multilevel Preconditioners
• Differentiation with Respect to the Domain in Boundary Value Problems
• The domain derivative and two applications in inverse scattering theory
• Frechet differentiability of boundary integral operators in inverse acoustic scattering
• A Robust Finite Element Method for Nonhomogeneous Dirichlet Problems in Domains with Curved Boundaries
• Boundary integral representations of second derivatives in shape optimization
• Integration von Funktionen, deren Werte die Elemente eines Vektorraumes sind
• Analysis of linear difference schemes in the sparse grid combination technique
• Sparse grids
• First order $k$-th moment finite element analysis of nonlinear operator equations with stochastic data
• First order second moment analysis for stochastic interface problems based on low-rank approximation