Advanced numerical methods for the numerical solution of partial differential equations that appear when modeling fluid flow in heterogeneous porous media are designed and analyzed from the mathematical, numerical and computational point of view. Furthermore, differential equations in general and especially complicated nonlinear differential equations are considered. These models are impossible to solve analytically and very complicated to solve numerically due to the presence of multiple scales in the coefficients representing the properties of the porous medium. Typical applications appear, among others, in petroleum and composite engineering applications. The numerical methods studied are of the type of multiscale finite element methods and domain decomposition methods.

• DOMAIN DECOMPOSITION
• NUMERICAL ANALYSIS
• FINITE ELEMENT METHODS
• APPLIED ANALYSIS