Submitted

  • L.F. Gatica and F.A. Sequeira: A priori and a posteriori error analyses of a HDG method for the Brinkman problem. Preprint 2017-04,  Centro de Investigación en Ingeniería Matemática, Universidad de Concepción, (2017).

  • L.F. Gatica, R. Oyarzúa and N. Sánchez: A priori and a posteriori error analyses of a augmented mixed-FEM for the Navier-Stokes-Brinkman problem. Preprint 2016-27,  Centro de Investigación en Ingeniería Matemática, Universidad de Concepción, (2016).

  • 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

  • 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).