Inclusion method of optimal constant with quadratic convergence for \(H_0^1\)-projection error estimates and its applications
type: Item
instance of: scholarly article
title: Inclusion method of optimal constant with quadratic convergence for \(H_0^1\)-projection error estimates and its applications
zbMATH Open document ID: 1496.65221
author: Takehiko Kinoshita
author: Yoshitaka Watanabe
author: Nobito Yamamoto
author: Mitsuhiro T. Nakao
published in: Journal of Computational and Applied Mathematics
publication date: 2022-10-06T00:00:00Z
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 33C45
Mathematics Subject Classification ID: 42C05
Mathematics Subject Classification ID: 47F05
Mathematics Subject Classification ID: 65G20
Mathematics Subject Classification ID: 65N15
zbMATH DE Number: 7596819
zbMATH Keywords: Poisson equation
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: finite element method
zbMATH Keywords: a priori error estimates
zbMATH Keywords: numerical verification
describes a project that uses: INTLAB
Wikidata QID: Q113878697
MaRDI profile type: Publication
full work available at URL: j.cam.2022.114521
OpenAlex ID: W4285606981
cites work: Elliptic partial differential equations of second order
cites work: Q3470840
cites work: Q4023365
cites work: Modification of dimension-splitting methods—overcoming the order reduction due to corner singularities
cites work: Compatibility conditions for Dirichlet and Neumann problems of Poisson's equation on a rectangle
cites work: Estimation of interpolation error constants for the \(P_0\) and \(P_1\) triangular finite elements
cites work: A priori error estimates for Lagrange interpolation on triangles.
cites work: A constructive a priori error estimation for finite element discretizations in a non-convex domain using singular functions
cites work: Q4100478
cites work: Numerical Verification Methods and Computer-Assisted Proofs for Partial Differential Equations
cites work: Computer-assisted proofs in PDE: a survey
cites work: Rigorous Numerics in Dynamics
cites work: Techniques of scientific computing (Part 2)
cites work: On very accurate enclosure of the optimal constant in the a priori error estimates for \(H_0^2\)-projection
cites work: On very accurate verification of solutions for boundary value problems by using spectral methods
cites work: Q4448960
cites work: Q3165673
cites work: On the best constant in the error bound for the \(H_0^1\)-projection into piecewise polynomial spaces
cites work: The Mathematical Theory of Finite Element Methods
cites work: $$H^3$$ and $$H^4$$ Regularities of the Poisson Equation on Polygonal Domains
cites work: Some remarks on a priori estimates of highly regular solutions for the Poisson equation in polygonal domains
cites work: Q4284594
cites work: Q4162607
cites work: Q3345690
cites work: Derived eigenvalues of symmetric matrices, with applications to distance geometry
cites work: Introduction to Interval Analysis
cites work: Verification methods: rigorous results using floating-point arithmetic
cites work: NUMERICAL VERIFICATION METHODS FOR SOLUTIONS OF ORDINARY AND PARTIAL DIFFERENTIAL EQUATIONS
cites work: A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration
cites work: Numerical verifications of solutions for elliptic equations in nonconvex polygonal domains
cites work: Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element
cites work: Numerical verification of solutions for nonlinear elliptic problems using an \(L^\infty\) residual method
cites work: Q4949347
DOI: 10.1016/J.CAM.2022.114521
description: scientific article; zbMATH DE number 7596819