Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element

DOI10.1016/0377-0427(94)00096-JzbMath0832.65123OpenAlexW2042568701MaRDI QIDQ1900766

Publication date: 11 March 1996

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

Full work available at URL: https://doi.org/10.1016/0377-0427(94)00096-j

zbMATH Keywords

finite element weakly nonlinear elliptic equations residual iteration

Mathematics Subject Classification ID

Numerical computation of solutions to systems of equations (65H10) Nonlinear boundary value problems for linear elliptic equations (35J65) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30)

Related Items

An Approach to The Numerical Verification of Solutions for Nonlinear Elliptic Problems With Local Uniqueness, Some remarks on the behaviour of the finite element solution in nonsmooth domains, Computer-assisted proofs for semilinear elliptic boundary value problems, Numerical verification method for infinite dimensional eigenvalue problems, Rigorous enclosures of solutions of Neumann boundary value problems, Numerical verification for solutions to partial differential equations, Numerical verification of solutions for nonlinear elliptic problems using an \(L^\infty\) residual method, Computer Assisted Fourier Analysis in Sequence Spaces of Varying Regularity, A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration, An enclosure method of eigenvalues for the elliptic operator linearized at an exact solution of nonlinear problems, Generalized Lyapunov-Schmidt reduction for parametrized equations at near singular points, Computer-assisted enclosure methods for elliptic differential equations, On very accurate enclosure of the optimal constant in the a priori error estimates for \(H_0^2\)-projection, Numerical verifications for eigenvalues of second-order elliptic operators, A numerical method to verify the invertibility of linear elliptic operators with applications to nonlinear problems, Global smooth solution curves using rigorous branch following, NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS, A computer-assisted existence and multiplicity proof for travelling waves in a nonlinearly supported beam, Verified numerical computations for an inverse elliptic eigenvalue problem with finite data, A numerical verification method for solutions of singularly perturbed problems with nonlinearity, A numerical proof algorithm for the non-existence of solutions to elliptic boundary value problems, On the best constant in the error bound for the \(H_0^1\)-projection into piecewise polynomial spaces, Numerical verification of solutions for obstacle problems using a Newton-like method, Numerical verification of solutions for elasto-plastic torsion problems, Computer-assisted proofs in PDE: a survey, A Theorem for Numerical Verification on Local Uniqueness of Solutions to Fixed-Point Equations, Orbital stability investigations for travelling waves in a nonlinearly supported beam, A posteriori and constructive a priori error bounds for finite element solutions of the Stokes equations, Inclusion method of optimal constant with quadratic convergence for \(H_0^1\)-projection error estimates and its applications, Computational proofs of the existence of solutions to elasto-plastic torsion problems, Finite element approximation of invariant manifolds by the parameterization method, Numerical verification of solutions for variational inequalities of the second kind

Cites Work