Inclusion method of optimal constant with quadratic convergence for \(H_0^1\)-projection error estimates and its applications
DOI10.1016/j.cam.2022.114521zbMath1496.65221OpenAlexW4285606981WikidataQ113878697 ScholiaQ113878697MaRDI QIDQ2088756
Nobito Yamamoto, Yoshitaka Watanabe, Takehiko Kinoshita, Mitsuhiro T. Nakao
Publication date: 6 October 2022
Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1016/j.cam.2022.114521
finite element methodorthogonal polynomialsPoisson equationnumerical verificationa priori error estimates
Error bounds for boundary value problems involving PDEs (65N15) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) General theory of partial differential operators (47F05) Algorithms with automatic result verification (65G20)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Compatibility conditions for Dirichlet and Neumann problems of Poisson's equation on a rectangle
- A priori error estimates for Lagrange interpolation on triangles.
- A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration
- A constructive a priori error estimation for finite element discretizations in a non-convex domain using singular functions
- Derived eigenvalues of symmetric matrices, with applications to distance geometry
- On very accurate enclosure of the optimal constant in the a priori error estimates for \(H_0^2\)-projection
- Estimation of interpolation error constants for the \(P_0\) and \(P_1\) triangular finite elements
- On the best constant in the error bound for the \(H_0^1\)-projection into piecewise polynomial spaces
- Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains
- Techniques of scientific computing (Part 2)
- Numerical verification of solutions for nonlinear elliptic problems using an \(L^\infty\) residual method
- Elliptic partial differential equations of second order
- Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element
- Computer-assisted proofs in PDE: a survey
- Some remarks on a priori estimates of highly regular solutions for the Poisson equation in polygonal domains
- NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
- $$H^3$$ and $$H^4$$ Regularities of the Poisson Equation on Polygonal Domains
- On very accurate verification of solutions for boundary value problems by using spectral methods
- Verification methods: Rigorous results using floating-point arithmetic
- Modification of dimension-splitting methods—overcoming the order reduction due to corner singularities
- Introduction to Interval Analysis
- Rigorous Numerics in Dynamics
- Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations
- The Mathematical Theory of Finite Element Methods
This page was built for publication: Inclusion method of optimal constant with quadratic convergence for \(H_0^1\)-projection error estimates and its applications
