A simple introduction to the mixed finite element method

GN Gatica - Theory and Applications. Springer Briefs in …, 2014 - Springer
The main purpose of this monograph is to provide a simple and accessible introduction to
the mixed finite element method as a fundamental tool to numerically solve a wide class of …

Locking-free finite element methods for poroelasticity

R Oyarzúa, R Ruiz-Baier - SIAM Journal on Numerical Analysis, 2016 - SIAM
We propose a new formulation along with a family of finite element schemes for the
approximation of the interaction between fluid motion and linear mechanical response of a …

New fully-mixed finite element methods for the Stokes–Darcy coupling

J Camano, GN Gatica, R Oyarzúa, R Ruiz-Baier… - Computer Methods in …, 2015 - Elsevier
In this paper we introduce and analyze two new fully-mixed variational formulations for the
coupling of fluid flow with porous media flow. Flows are governed by the Stokes and Darcy …

Boundary integral equation methods for the two-dimensional fluid-solid interaction problem

T Yin, GC Hsiao, L Xu - SIAM Journal on Numerical Analysis, 2017 - SIAM
This paper is concerned with boundary integral equation methods for solving the two-
dimensional fluid-solid interaction problem. We reduce the problem to three different …

A fully-mixed finite element method for the Navier–Stokes/Darcy coupled problem with nonlinear viscosity

S Caucao, GN Gatica, R Oyarzúa… - Journal of Numerical …, 2017 - degruyter.com
We propose and analyze an augmented mixed finite element method for the coupling of fluid
flow with porous media flow. The flows are governed by a class of nonlinear Navier–Stokes …

[图书][B] Introducción al análisis funcional: teoría y aplicaciones

GN Gatica - 2024 - books.google.com
Este libro aborda los resultados clave del Análisis Funcional y sus aplicaciones en
Matemática, Física e Ingeniería. Está diseñado como texto y obra de consulta, dirigido a …

A vorticity-based fully-mixed formulation for the 3D Brinkman–Darcy problem

M Alvarez, GN Gatica, R Ruiz-Baier - Computer Methods in Applied …, 2016 - Elsevier
We propose and analyze a fully-mixed finite element method to numerically approximate the
flow patterns of a viscous fluid within a highly permeable medium (an array of low …

Analysis of the coupling of Lagrange and Arnold--Falk--Winther finite elements for a fluid-solid interaction problem in three dimensions

GN Gatica, A Márquez, S Meddahi - SIAM Journal on Numerical Analysis, 2012 - SIAM
We introduce and analyze a new finite element method for a three-dimensional fluid-solid
interaction problem. The media are governed by the acoustic and elastodynamic equations …

Solution of coupled acoustic–elastic wave propagation problems with anelastic attenuation using automatic hp-adaptivity

PJ Matuszyk, LF Demkowicz, C Torres-Verdin - Computer Methods in …, 2012 - Elsevier
The paper presents a frequency-domain hp-adaptive finite element (FE) method for a class
of coupled (visco-) acoustics/anelasticity problems with application to modeling of sonic …

Pure vorticity formulation and Galerkin discretization for the Brinkman equations

V Anaya, D Mora, R Ruiz-Baier - IMA Journal of Numerical …, 2017 - academic.oup.com
We introduce a new finite element method for the approximation of the three-dimensional
Brinkman problem formulated in terms of the velocity, vorticity and pressure fields. The …