In this work we deal with the efficient solution of the large sparse systems of equations arising from the discretization of partial differential equations. This issue is one of the most important aspects in the numerical solution of many problems, and therefore it deserves important attention. With this purpose, our primary interest here is to design efficient finite element geometric multigrid methods on semi-structured triangular grids. To this end, a local Fourier analysis on triangular grids is presented, resulting in a very useful tool to choose suitable components of multigrid methods. The practical utility of this approach is illustrated with some examples of scalar and vector problems.

Carmen Rodrigo obtained her degree in Mathematics at University of Zaragoza in 2005. In 2010 she received her PhD with distinction and with the European mention at the same University. Her PhD was also selected by SEMA (Spanish Society of Applied Mathematics) as finalist of 2010 ECCOMAS PhD Award. Currently, she has an Assistant Professor position at the Department of Applied Mathematics at the University of Zaragoza, and recently she has been honored with the SEMA Award "Antonio Valle" to Young Researchers 2015. Her research has been focused on numerical methods for partial differential equations and the study of iterative methods for solving the related systems of algebraic equations obtained from the discretization of the original system. More precisely, deep contributions on the design and applications of multigrid methods centering in the study of the convergence via local Fourier analysis. Also she is interested in problems related to poroelastic models in their different areas of application.