This work is concerned with the devising and the analysis of hybrid discretization methods for nonlinear
variational inequalities arising in computational mechanics. Salient advantages of such methods are:
local conservation at the cell level,
robustness in different regimes
and the possibility to use polygonal/polyhedral
meshes with hanging nodes (very attractive for mesh adaptation).
methods are based on discrete unknowns attached to the mesh faces and to the mesh
cells, the latter ones can be eliminated locally by static condensation. Two main applications of
hybrid discretizations methods are addressed: 1) Signorini's unilateral contact problem.
We prove optimal error estimates leading to energy-error convergence rates of order (k+1)
Viscoplastic yield flows.
We devise a discrete augmented Lagrangian method applied to the present hybrid discretization. We exploit
the capability of hybrid methods to use polygonal meshes with hanging nodes to perform local mesh
adaptation and better capture the yield surface. The accuracy and performance of the present schemes
is assessed on bi-dimensional test cases including comparisons with the literature.
M.S. Mechanical Engineering (09/2014), Universidad Nacional de Colombia, Colombia.
Dissertation: Use of the local discontinuous Galerkin method with temporal integration by the ExGA method.
Advisor: Diego Alexander Garzón.
Hybrid High-Order discretizations combined with Nitsche's
method for Dirichlet and Signorini boundary conditions.
[hal] K. Cascavita, F. Chouly, A. Ern.
Accepted subject to minor revisions at IMA Journal of Numerical Analysis.
Hybrid discretization methods with adaptive yield surface detection for Bingham pipe flows [hal] K. Cascavita, J. Bleyer, X. Chateau, A. Ern.
Journal of Scientific Computing, 77 (3): 1424-1443, 2018.
Hybrid discretization methods for Bingham vector flows.
K. Cascavita, J. Bleyer, X. Chateau, A. Ern.
Paper in preparation
A local discontinuous Galerkin method using an Explicit Green approach(ExGA) for the linear heat equation. K. Cascavita, D.A. Garzón.
Paper in preparation
Numerical solution of the incompressible Navier-Stokes equations with finite volume method (in Spanish). [Scielo] K. Cascavita, J.E. Jaramillo, F. Fonseca.
Rev. Ion. 2013, vol. 26, n.2, pp.17-29.
89th International Association of Applied Mathematics and Mechanics Annual meeting (GAMM), Munich (Germany), 03/2018. [PDF]
16th European Finite Element Fair (EFEF), Heidelberg (Germany), 06/2018.
6th European conference on Computational Mechanics (ECCM), Glasgow (UK), 06/2018. [PDF]
13th World Congress in Computational Mechanics (WCCM), New York (USA), 07/2018. [PDF]
1st Conference on
Complexity Analysis of Industrial Systems and Advanced Modeling (CAISAM), Ben Guerir,
17th European Finite Element Fair (EFEF), Nicosa (Chipre), 05/2019.
Poster contribution, Labex MMCD Atelier Bilan et Perspectives, Champs sur Marne (France), 09/2016. [PDF]
Young Researchers Seminar, Champs sur Marne (France), 03/2017.