Neural network approach for solving nonlocal boundary value problems

V Palade, MS Petrov, TD Todorov - Neural Computing and Applications, 2020 - Springer
This paper proposes a radial basis function (RBF) network-based method for solving a
nonlinear second-order elliptic equation with Dirichlet boundary conditions. The nonlocal …

Finite-element domain approximation for Maxwell variational problems on curved domains

R Aylwin, C Jerez-Hanckes - SIAM Journal on Numerical Analysis, 2023 - SIAM
We consider the problem of domain approximation in finite element methods for Maxwell
equations on general curved domains, ie, when affine or polynomial meshes fail to exactly …

A theoretical analysis of the deposition of colloidal particles from a volatile liquid meniscus in a rectangular chamber

A Zigelman, O Manor - Colloids and Surfaces A: Physicochemical and …, 2018 - Elsevier
Traditionally, experiments of pattern deposition are conducted using volatile suspensions or
solutions in sessile drops. However, several recent studies on the pattern deposition of …

The Steklov eigenvalue problem in a cuspidal domain

MG Armentano, AL Lombardi - Numerische Mathematik, 2020 - Springer
In this paper we analyze the approximation, by piecewise linear finite elements, of a Steklov
eigenvalue problem in a plane domain with an external cusp. This problem is not covered by …

Eigenvalue problems in a non-Lipschitz domain

G Acosta, MG Armentano - IMA Journal of Numerical Analysis, 2014 - ieeexplore.ieee.org
In this paper we analyse piecewise linear finite element approximations of the Laplace
eigenvalue problem in the plane domain Ω={(x, y): 0< x< 1, 0< y< x α}, which gives for 1< α …

Extension theorems for external cusps with minimal regularity

G Acosta, I Ojea - Pacific Journal of Mathematics, 2012 - msp.org
Sobolev functions defined on certain simple domains with an isolated singular point (such
as power type external cusps) can not be extended in standard, but in appropriate weighted …

SOME EIGENVALUE PROBLEMS IN NON-LIPSCHITZ DOMAINS

G ACOSTA, MG ARMENTANO - ci2ma.udec.cl
The goal of this talk is the analysis of piecewise linear finite element approximations of
spectral problems in a plane domain Ω={(x; y): 0< x< 1; 0< y< xα}; which gives, for α> 1, the …

Eigenvalue problems in a non-Lipschitz domain

G Acosta Rodriguez, MG Armentano - 2013 - ri.conicet.gov.ar
In this paper we analyse piecewise linear finite element approximations of the Laplace
eigenvalue problem in the plane domain Ω={(x, y): 0< x< 1, 0< y< xα}, which gives for 1< α …