Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-Bénard problem
DOI10.1007/BF03186543zbMath1184.65106OpenAlexW2077303265MaRDI QIDQ849191
Mitsuhiro T. Nakao, Yoshitaka Watanabe
Publication date: 25 February 2010
Published in: Japan Journal of Industrial and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://projecteuclid.org/euclid.jjiam/1265033790
error estimatesfinite element methodelliptic equationsRayleigh-Bénard problembifurcation pointheat convection problemsnumerical verification method
Probabilistic models, generic numerical methods in probability and statistics (65C20) Error bounds for boundary value problems involving PDEs (65N15) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Bifurcations in context of PDEs (35B32) Nonlinear boundary value problems for nonlinear elliptic equations (35J66)
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- Numerical verification of stationary solutions for Navier-Stokes problems
- A numerical verification method of bifurcating solutions for 3-dimensional Rayleigh-Bénard problems
- On the solution of interval linear systems
- Explicit \(H_ 2\)-estimates and pointwise bounds for solutions of second- order elliptic boundary value problems
- On the best constant in the error bound for the \(H_0^1\)-projection into piecewise polynomial spaces
- A note on epsilon-inflation
- PROFIL/BIAS - A fast interval library
- The Eckhaus criterion for convection roll solutions of the Oberbeck-Boussinesq equations
- Some computer assisted proofs for solutions of the heat convection problems
- A numerical verification of nontrivial solutions for the heat convection problem
- A symmetry-breaking bifurcation theorem and some related theorems applicable to maps having unbounded derivatives
- A computer-assisted proof for the Kolmogorov flows of incompressible viscous fluid
- An efficient approach to the numerical verification for solutions of elliptic differential equations
- A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems
- Determination of the Babuska-Aziz constant for the linear triangular finite element
- On the stability of the Boussinesq equations
- Existence and nonuniqueness of rectangular solutions of the Benard problem
- NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
- A numerical approach to the proof of existence of solutions for elliptic problems
- Bounded Solutions of Finite Dimensional Approximations to the Boussinesq Equations
- A Numerical Verification Method for Solutions of Boundary Value Problems with Local Uniqueness by Banach's Fixed-Point Theorem
- An Approach to The Numerical Verification of Solutions for Nonlinear Elliptic Problems With Local Uniqueness
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