On the convergence of the Newton-GMBACK method
AbstractWhen the GMBACK solver is used in the Newton iterates, the iterates may be written either as inexact Newton iterates…
Numerical Analysis
Analytic vs. numerical solutions to a Sturm-Liouville transmission eigenproblem
AbstractAn elliptic one-dimensional second order boundary value problem involving discontinuous coefficients, with or without transmission conditions, is considered. For the…
Benchmark for numerical solutions of flow in heterogeneous groundwater formations
AbstractThis article presents numerical investigations on accuracy and convergence properties of several numerical approaches for simulating steady state flows in…
Natural convection from a vertical plate embedded in a non-Darcy bidisperse porous medium
Abstract This paper studies the steady, free convection boundary layer flow about a vertical, isothermal plate embedded in a non-Darcy…
A stabilized finite element method for inverse problems subject to the convection-diffusion equation. I: diffusion-dominated regime
AbstractThe numerical approximation of an inverse problem subject to the convection–diffusion equation when diffusion dominates is studied. We derive Carleman…
Unique continuation for the Helmholtz equation using stabilized finite element methods
AbstractIn this work we consider the computational approximation of a unique continuation problem for the Helmholtz equation using a stabilized finite element…
Accurate Chebyshev collocation solutions for the biharmonic eigenproblem on a rectangle
AbstractWe are concerned with accurate Chebyshev collocation (ChC) solutions to fourth order eigenvalue problems. We consider the 1D case as…
Invariant sets and attractors for Hanusse-type chemical systems with diffusions
AbstractWe are concerned with Hanusse-type chemical models with diffusions. We show that some bounded invariant sets ⊂R^{N} found for the…
An extension of the second order dynamical system that models Nesterov’s convex gradient method
Abstract In this paper we deal with a general second order continuous dynamical system associated to a convex minimization problem…
New optimization algorithms for neural network training using operator splitting techniques
AbstractWe present a new type of optimization algorithms, adapted for neural network training. These algorithms are based upon sequential operator…