## Research Abstracts Online

January
2008 - March 2009

### University of Minnesota Twin Cities

Institute of Technology

School of Mathematics

## PI: Bernardo Cockburn, Fellow

### Numerical Methods for Partial Differential Equations

These researchers used the supercomputers for two projects during this period. The first project dealt with obtaining superconvergent approximations of linear functions, considering ordinary differential equations and convection-diffusion equation model problems. The method is based on approximations given by the discontinuous Galerkin methods of the primal and its adjoint problems, and their post-processings. The approximate functionals have the order to convergence nearly four times that of the numerical solutions. The second project studied hybridization of the finite element methods for various problems.

### Group Members

Johnny Guzman, Research Associate

Ryuhei "Drew” Ichikawa, Graduate Student