Information-based numerical practice

DOI10.1016/0885-064X(87)90019-7zbMath0644.65017MaRDI QIDQ1102700

Ivo M. Babuška

Publication date: 1987

Published in: Journal of Complexity (Search for Journal in Brave)

zbMATH Keywords

finite element methodfeedbackbibliographyquadrature formulaereliability assessmentODE solversselection of nonadaptive methods

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Roundoff error (65G50) Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations (65L60) Numerical solution of boundary value problems involving ordinary differential equations (65L10) Approximate quadratures (41A55) Numerical quadrature and cubature formulas (65D32)

Related Items

Some basic information on information-based complexity theory ⋮ Perspectives on information-based complexity

Cites Work

• Basic principles of feedback and adaptive approaches in the finite element method
• Feedback and adaptive finite element solution of one-dimensional boundary value problems
• A feedback finite element method with a posteriori error estimation. I: The finite element method and some basic properties of the a posteriori error estimator
• A survey of information-based complexity
• Quality assessment and control of finite element solutions
• The h-p version of the finite element method. I. The basic approximation results
• The h-p version of the finite element method. II. General results and applications
• An expert-system-like feedback approach to the hp-version of the finite element method
• The h, p and h-p versions of the finite element method in 1 dimension. III. The adaptive h-p version
• The $h-p$ version of the finite element method with quasiuniform meshes
• Optimization of numerical processes
• On universal optimal quadrature formulae
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