Name: RIEDSON BAPTISTA

Publication date: 17/12/2020
Advisor:

Namesort descending Role
ISAAC PINHEIRO DOS SANTOS Co-advisor *
LUCIA CATABRIGA Advisor *

Examining board:

Namesort descending Role
ISAAC PINHEIRO DOS SANTOS Co advisor *
LUCIA CATABRIGA Advisor *
MARIA CLAUDIA SILVA BOERES Internal Examiner *

Summary: In this work, we present a nonlinear variational multiscale finite element method to solve
the incompressible Navier-Stokes equations. The method is based on a decomposition in
two levels of the approximation space and the local problem is modified by introducing an
artificial diffusion that acts in an adaptive way only on the unresolved discretization scales.
It can be considered a self-adaptive method, so that the amount of sub-mesh viscosity is
automatically introduced according to the residue of the scales resolved at the element
level. To reduce the computational cost typical of two-scale methods, the micro-scale
space is defined through polynomial functions that cancel each other out at the border
of the elements, known as bubble functions, whose degrees of freedom are eliminated
locally in favor of the degrees of freedom that reside on the resolved scales. We compared
the numerical and computational performance of the method with the results obtained
with the formulation streamline-upwind/Petrov-Galerkin (SUPG) combined with the
method pressure stabilizing/Petrov-Galerkin (PSPG) through a set of four two-dimensional
reference problems.
Keywords: Finite element. Multiscale estabilized methods. Incompressible Navier-Stokes
equations.

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