The present research areas of Gabriel N. Gatica refer to the mathematical and numerical analysis of linear and nonlinear boundary value problems in potential theory, electromagnetism, elasticity, and fluid mechanics, in interior as well as in exterior regions.

The following tools are employed (mainly):

• FINITE ELEMENT METHODS
• BOUNDARY INTEGRAL EQUATION METHODS
• DISCONTINUOUS GALERKIN METHODS
• DIRICHLET-TO-NEUMANN MAPPINGS
• LEAST SQUARES METHODS
• PRIMAL AND DUAL-MIXED FORMULATIONS 

The following objectives are sought:

• EXISTENCE AND UNIQUENESS OF CONTINUOUS SOLUTIONS
• EXISTENCE AND UNIQUENESS OF DISCRETE SOLUTIONS
• A-PRIORI AND A-POSTERIORI ERROR ESTIMATES
• FULLY DISCRETE SCHEMES
• EFFICIENT ALGORITHMS AND COMPUTATIONAL IMPLEMENTATIONS