Extrapolation, combination, and sparse grid techniques for elliptic boundary value problems

DOI10.1016/S0045-7825(94)80029-4zbMath0824.65104OpenAlexW2068987297MaRDI QIDQ1892467

Michael Griebel, Ulrich Rüde, Hans-Joachim Bungartz

Publication date: 14 June 1995

Published in: Computer Methods in Applied Mechanics and Engineering (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/s0045-7825(94)80029-4

zbMATH Keywords

Dirichlet problemPoisson equationRichardson's extrapolationcombination techniquesparse grid finite element method

Mathematics Subject Classification ID

Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)

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Two-scale sparse finite element approximations, Adaptive sparse grid algorithms with applications to electromagnetic scattering under uncertainty, Optimal scaling parameters for sparse grid discretizations, Multiscale simulation of polymeric fluids using the sparse grid combination technique, Two-scale finite element discretizations for nonlinear eigenvalue problems in quantum physics, Three-scale finite element eigenvalue discretizations, On the computation of the eigenproblems of hydrogen and helium in strong magnetic and electric fields with the sparse grid combination technique, The combination technique for a two-dimensional convection-diffusion problem with exponential layers, Adaptive Sparse Grids and Extrapolation Techniques, Fitting multidimensional data using gradient penalties and the sparse grid combination technique, Fast Boolean approximation methods for solving integral equations in high dimensions

Cites Work

• Asymptotic error expansion and Richardson extrapolation for linear finite elements
• Asymptotic expansions of the discretization error of boundary value problems of the Laplace equation in rectangular domains
• Transfinite element methods: Blending-function interpolation over arbitrary curved element domains
• On theh- andp-Versions of the Extrapolated Gordon’s Projector with Applications to Elliptic Equations
• The Hierarchical Basis Extrapolation Method
• Fully Adaptive Multigrid Methods
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