A proof via finite elements for Schiffer's conjecture on a regular pentagon
type: Item
instance of: scholarly article
title: A proof via finite elements for Schiffer's conjecture on a regular pentagon
zbMATH Open document ID: 1456.65165
author: Nilima Nigam
author: Bartłomiej Andrzej Siudeja
author: Benjamin Young
published in: Foundations of Computational Mathematics
publication date: 2021-01-06T00:00:00Z
review text: The authors show that there exists a Neumann eigenfunction on a regular pentagon that is positive on the boundary and not identically constant. The proof of this result consists in blending ideas from analysis, optimization and numerical analysis (approximation theory techniques), and it is an interesting contribution in its own right. The proof itself is human-readable and fully analytic except for the matrix eigenvalue computations on 20 large matrices from the strategy for computing discrete eigenvalues and from the lower bound estimation for the smallest eigenvalue of a sparse matrix. The excepted part is of course a computed assisted proof. The authors have found a rather short proof certificate for this computed proof, show that it is checkable and adaptable.
Mathematics Subject Classification ID: 65N30
Mathematics Subject Classification ID: 35B05
Mathematics Subject Classification ID: 35P15
Mathematics Subject Classification ID: 68T05
zbMATH DE Number: 7290665
zbMATH Keywords: Laplacian
zbMATH Keywords: 2D domain
zbMATH Keywords: Neumann eigenproblem
zbMATH Keywords: nonconforming finite element
zbMATH Keywords: eigenvalue bound
zbMATH Keywords: nodal line
zbMATH Keywords: learning algorithm
zbMATH Keywords: computer proof
Wikidata QID: Q114228269
reviewed by: Calin Ioan Gheorghiu
describes a project that uses: FEniCS
describes a project that uses: SymPy
describes a project that uses: SyFi
describes a project that uses: mpmath
describes a project that uses: SciPy
describes a project that uses: CHOLMOD
describes a project that uses: SageMath
describes a project that uses: FreeFem++
describes a project that uses: INTLAB
MaRDI profile type: Publication
full work available at URL: s10208-020-09447-y
OpenAlex ID: W3007906496
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DOI: 10.1007/S10208-020-09447-Y
description: scientific article; zbMATH DE number 7290665