A priori error estimates of finite element solutions of parametrized strongly nonlinear boundary value problems

DOI10.1016/S0377-0427(96)00149-5zbMath0883.65051WikidataQ126552125 ScholiaQ126552125MaRDI QIDQ678809

Takuya Tsuchiya, Ivo M. Babuška

Publication date: 23 March 1998

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

Sobolev spaceerror estimatesfinite elementnonlinear boundary value problemFredholm operatorturning pointsstrongly nonlinear problems

Mathematics Subject Classification ID

Iterative procedures involving nonlinear operators (47J25) Nonlinear differential equations in abstract spaces (34G20) Numerical solutions to equations with nonlinear operators (65J15) Numerical solution of boundary value problems involving ordinary differential equations (65L10)

Related Items (7)

Yamamoto's principle and its applications to precise finite element error analysis. ⋮ Numerical verification of solutions of parametrized nonlinear boundary value problems with turning points ⋮ Dimension reduction in stochastic modeling of coupled problems ⋮ Error estimates and adaptive finite element methods ⋮ Finite element analysis for parametrized nonlinear equations around turning points ⋮ Estimating spatial and parameter error in parameterized nonlinear reaction–diffusion equations ⋮ Finite element approximations of parametrized strongly nonlinear boundary value problems.

Uses Software

• PITCON

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
• Solution manifolds and submanifolds of parametrized equations and their discretization errors
• On the monotone convergence of Newton's method
• Singularities and groups in bifurcation theory. Volume I
• Finite dimensional approximation of nonlinear problems. I: Branches of nonsingular solutions
• On the Discretization Error of Parametrized Nonlinear Equations
• Maximum norm error estimates in the finite element method with isoparametric quadratic elements and numerical integration

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