Marcio Bortoloti

Marcio Bortoloti

Departamento de Ciências Exatas e Tecnológicas, Universidade Estadual do Sudoeste da Bahia

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A stabilized finite element method to pseudoplasticflow governed by the Sisko relation

Published in Computational & Applied Mathematics, 2012

In this work, a consistent stabilized mixed finite element formulation for incompressible pseudoplastic fluid flows governed by the Sisko constitutive equation is mathematically analysed. This formulation is constructed by adding least-squares of the governing equations and of the incompressibility constraint, with discontinuous pressure approximations, allowing the use of same order interpolations for the velocity and the pressure. Numerical results are presented to confirm the mathematical stability analysis.

Recommended citation: Your Name, You. (2010). "Paper Title Number 2." Journal 1. 1(2). https://www.scielo.br/j/cam/a/vkL8fspCCqgp9wDRmBzQwdg/?format=pdf&lang=en

A stabilized finite element analysis for a power-law pseudoplastic Stokes problem

Published in Applicable Analysis: An International Journal, 2015

In this work, we present a mixed stabilized finite element formulation in primitive variables, for an incompressible stationary generalized Stokes problem for pseudoplastic flow governed by the Power-Law model. The mixed formulation is constructed by adding least squares of the governing equations to the classical Galerkin formulation, with continuous interpolations for the velocity and discontinuous interpolations for the pressure. A finite element analysis is presented establishing stability conditions and finding error estimates. Numerical results are presented to show the good performance of this formulation and to confirm the mathematical estimates obtained.

Recommended citation: Your Name, You. (2015). "Paper Title Number 3." Journal 1. 1(3). https://www.tandfonline.com/doi/abs/10.1080/00036811.2015.1009900?journalCode=gapa20&

Damped Newton’s method on Riemannian manifolds

Published in Journal of Global Optimization, 2020

A damped Newton’s method to find a singularity of a vector field in Riemannian setting is presented with global convergence study. It is ensured that the sequence generated by the proposed method reduces to a sequence generated by the Riemannian version of the classical Newton’s method after a finite number of iterations, consequently its convergence rate is superlinear/quadratic. Even at an early stage of development, we can observe from numerical experiments that DNM presented promising results when compared with the well known BFGS and Trust Regions methods. Moreover, damped Newton’s method present better performance than the Newton’s method in number of iteration and computational time.

Recommended citation: Your Name, You. (2015). "Paper Title Number 3." Journal 1. 1(3). https://doi.org/10.1007/s10898-020-00885-0

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