A numerical approach to the proof of existence of solutions for elliptic problems
From MaRDI portal
Publication:3469483
DOI10.1007/BF03167877zbMath0694.35051MaRDI QIDQ3469483
Publication date: 1988
Published in: Japan Journal of Applied Mathematics (Search for Journal in Brave)
Boundary value problems for second-order elliptic equations (35J25) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation (35J05)
Related Items
Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains ⋮ An efficient numerical verification method for the Kolmogorov problem of incompressible viscous fluid ⋮ Worst case error bounds for the solution of uncertain Poisson equations with mixed boundary conditions ⋮ On computational proofs of the existence of solutions to nonlinear parabolic problems ⋮ An Approach to The Numerical Verification of Solutions for Nonlinear Elliptic Problems With Local Uniqueness ⋮ Norm bound computation for inverses of linear operators in Hilbert spaces ⋮ Numerical verification method of solutions for elliptic equations and its application to the Rayleigh-Bénard problem ⋮ Numerical verification method for infinite dimensional eigenvalue problems ⋮ Numerical verification of existence and inclusion of solutions for nonlinear operator equations ⋮ Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element ⋮ Rigorous enclosures of solutions of Neumann boundary value problems ⋮ Numerical verification of solutions of parametrized nonlinear boundary value problems with turning points ⋮ Numerical verification for solutions to partial differential equations ⋮ A numerical approach to the proof of existence of solutions for elliptic problems II ⋮ Numerical verification of solutions for nonlinear elliptic problems using an \(L^\infty\) residual method ⋮ A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory ⋮ Validated numerical approximation of stable manifolds for parabolic partial differential equations ⋮ A computer‐assisted method for the diblock copolymer model ⋮ Interval versions of central-difference method for solving the Poisson equation in proper and directed interval arithmetic ⋮ Verified bounds for singular values, in particular for the spectral norm of a matrix and its inverse ⋮ Fast interval matrix multiplication ⋮ Numerical verification of solutions for obstacle problems. ⋮ A new formulation using the Schur complement for the numerical existence proof of solutions to elliptic problems: without direct estimation for an inverse of the linearized operator ⋮ Verified computations of solutions for nondifferentiable elliptic equations related to MHD equilibria ⋮ Guaranteed error bounds for finite element approximations of noncoercive elliptic problems and their applications ⋮ Certified error bounds for uncertain elliptic equations ⋮ A posteriori verification for the sign-change structure of solutions of elliptic partial differential equations ⋮ Numerical Verification Methods for Solutions of the Free Boundary Problem ⋮ Solving nonlinear parabolic problems with result verification. I: One- space dimensional case ⋮ A Numerical Verification Method for a System of FitzHugh-Nagumo Type ⋮ Error constants for the semi-discrete Galerkin approximation of the linear heat equation ⋮ A numerical verification method for the existence of weak solutions for nonlinear boundary value problems ⋮ Numerical verifications of solutions for nonlinear elliptic equations ⋮ An enclosure method of eigenvalues for the elliptic operator linearized at an exact solution of nonlinear problems ⋮ 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 ⋮ NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS ⋮ A numerical approach to the proof of existence of solutions for some generalized obstacle problems ⋮ Numerical verification for existence of a global-in-time solution to semilinear parabolic equations ⋮ Sharp numerical inclusion of the best constant for embedding \(H_0^1(\Omega) \hookrightarrow L^p(\Omega)\) on bounded convex domain ⋮ Numerical Verification for Elliptic Boundary Value Problem with Nonconforming $$\mathcal {P}_1$$ Finite Elements ⋮ Numerical verification method for positive solutions of elliptic problems ⋮ A numerical proof algorithm for the non-existence of solutions to elliptic boundary value problems ⋮ Numerical verifications of solutions for elliptic equations with strong nonlinearity ⋮ Rigorous numerical computations for 1D advection equations with variable coefficients ⋮ Numerical verification of solutions for elasto-plastic torsion problems ⋮ Computer-assisted proof for the stationary solution existence of the Navier-Stokes equation over 3D domains ⋮ Global dynamics in nonconservative nonlinear Schrödinger equations ⋮ A posteriori and constructive a priori error bounds for finite element solutions of the Stokes equations ⋮ Finite element approximation of invariant manifolds by the parameterization method ⋮ A computer-assisted method for excluding eigenvalues of an elliptic operator linearized at a solution of a nonlinear problem
Uses Software
Cites Work
