Submitted
- J. Camaño, L.F. Gatica and R. Oyarzúa:
A priori and a posteriori error analyses of a flux-based mixed-FEM for convection-diffusion-reaction problems.
Preprint 2016-25, Centro de Investigación en Ingeniería Matemática, Universidad de
Concepción, (2016).
Papers in Refereed Journals
- S. Caucao, G.N. Gatica and L.F. Gatica:
A Banach space-based mixed finite element method for the stationary convective Brinkman-Forchheimer problem.
Calcolo, vol. 60, 4, article: 51, (2023).
- V. Anaya, R. Caraballo, S. Caucao, L.F. Gatica, R. Ruiz-Baier and I. Yotov:
A vorticity-based mixed formulation for the unsteady Brinkman-Forchheimer equations.
Computer Methods in Applied Mechanics and Engineering, vol. 404, Art. Num. 115829, (2023).
- P.E. Farrell, L.F. Gatica, B. Lamichhane, R. Oyarzúa and R. Ruiz-Baier:
Mixed Kirchhoff stress - displacement - pressure formulations for incompressible hyperelasticity.
Computer Methods in Applied Mechanics and Engineering, vol. 374, 24 p., (2021) 113562.
- L.F. Gatica, R. Oyarzúa and Nestor Sánchez:
A priori and a posteriori error analysis of a augmented mixed-FEM for the Navier-Stokes-Brinkman problem.
Computers and Mathematics with Applications, vol. 75, 7, pp. 2420-2444, (2018).
- L.F. Gatica and F.A. Sequeira:
A priori and a posteriori error analyses of a HDG method for the Brinkman problem.
Computers and Mathematics with Applications, vol. 75, 4, pp. 1191-1212, (2018).
- G.N. Gatica, L.F. Gatica and F.A. Sequeira:
A priori and a posteriori error analyses of a pseudostress-based mixed formulation for linear elasticity.
Computers and Mathematics with Applications, vol. 71, 2, pp. 585-614, (2016).
- G.N. Gatica, L.F. Gatica and F.A. Sequeira:
A RT_k - P_k approximation for linear elasticity yielding a broken H(div) convergent postprocessed stress.
Applied Mathematics Letters, vol. 49, pp. 133-140, (2015).
- Z. Fu, L.F. Gatica and F.-J. Sayas:
Algorithm 949: MATLAB Tools for HDG in Three Dimensions.
ACM Transactions on Mathematical Software, vol. 41, 3, Article 20, (2015).
- G.N. Gatica, L.F. Gatica and F.A. Sequeira:
Analysis of an augmented pseudostress-based mixed formulation for a nonlinear Brinkman
model of porous media flow.
Computer Methods in Applied Mechanics and Engineering, vol. 289, 1, pp. 104-130, (2015).
- G.N. Gatica, L.F. Gatica and A. Marquez:
Analysis of a pseudostress-based mixed finite element method for the Brinkman model
of porous media flow. Numerische Mathematik, vol. 126, 4, pp. 635-677, (2014).
- G.N. Gatica, L.F. Gatica and A. Marquez:
Augmented mixed finite element methods for a vorticity-based velocity-pressure-stress formulation of the
Stokes problem in 2D.
International Journal for Numerical Methods in Fluids, vol. 67, 4, pp. 450-477, (2011).
- G.N. Gatica, L.F. Gatica and E.P. Stephan:
A dual-mixed finite element method for nonlinear incompressible elasticity
with mixed boundary conditions.
Computer Methods in Applied Mechanics and Engineering, vol. 196, 35-36, pp. 3348-3369, (2007).
- G.N. Gatica, L.F. Gatica: On the a-priori and a-posteriori error analysis of a two-fold saddle point approach for nonlinear incompressible
elasticity. International Journal for Numerical Methods in Engineering, vol. 68, 8,
pp. 861-892, (2006).
- T.P. Barrios, G.N. Gatica and , L.F. Gatica: On the numerical
analysis of a nonlinear elliptic problem via mixed-FEM and Lagrange
multipliers. Applied Numerical Mathematics, vol. 48, 2, pp.
135-155,
(2004).
- G.N. Gatica, L.F. Gatica and E.P. Stephan: AFEM-DtN formulation
for a nonlinear exterior problem in incompressible elasticity. Mathematical
Methods in the Applied Sciences, vol. 26, 2, pp. 151-170, (2003).
- L.F. Gatica: Sobre la Ecuación de Liénard de Grado 4. CUBO Revista de Matemática, vol. 12, pp. 39-50, (1997).
Dissertations
- Luis F. Gatica:
Métodos de elementos finitos mixtos para elasticidad incompresible no lineal. Ph.D. Dissertation, Universidad de Concepción, CHILE, (2005).
- Luis F. Gatica:
Sobre el número de ciclos límites de la ecuación
de Liénard polinomial. M.S. Dissertation, Universidad de Concepcion, CHILE, (1995).