Solution manifolds and submanifolds of parametrized equations and their discretization errors

DOI10.1007/BF01391412zbMath0555.65034OpenAlexW2067981301MaRDI QIDQ760765

James P. Fink, Werner C. Rheinboldt

Publication date: 1984

Published in: Numerische Mathematik (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/132971

zbMATH Keywords

Banach spacesFredholm operatordiscretization erroraugmented equationsnonlinear parameter-dependent equationspath- tracing proceduressolution manifolds

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Nonlinear boundary value problems for linear elliptic equations (35J65) Numerical solutions to equations with nonlinear operators (65J15)

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Cites Work

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• Finite dimensional approximation of nonlinear problems. II: Limit points
• Finite dimensional approximation of nonlinear problems. III: Simple bifurcation points
• Finite dimensional approximation of nonlinear problems. I: Branches of nonsingular solutions
• On the Discretization Error of Parametrized Nonlinear Equations
• Estimates near the boundary for solutions of elliptic partial differential equations satisfying general boundary conditions. I
• On the Error Behavior of the Reduced Basis Technique for Nonlinear Finite Element Approximations
• An Analysis of Upwind Schemes for the Navier–Stokes Equations
• NON-LINEAR FREDHOLM MAPS AND THE LERAY-SCHAUDER THEORY
• Approximative methods for nonlinear equations (two approaches to the convergence problem)
• THE METHODS OF LYAPUNOV AND SCHMIDT IN THE THEORY OF NON-LINEAR EQUATIONS AND THEIR FURTHER DEVELOPMENT

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