Numerical Study of the Zaremba Problem

S. D. Algazin^a^,*

^aIshlinsky Institute for Problems in Mechanics, Russian Academy of Sciences, Moscow, 119526 Russia

Correspondence to: *e-mail: algazinsd@mail.ru

Received 29 March, 2021

Abstract—We consider the eigenvalue problem for a two-dimensional Laplace operator with mixed boundary conditions (Zaremba problem), which (presumably) has a smooth solution inside the domain. Calculations show that the operator –Δ has a negative eigenvalue, i.e., it is not positive definite.

Keywords: numerical algorithms without saturation, Zaremba problem, eigenvalue problem with mixed boundary conditions

DOI: 10.1134/S1064562421050033