Brief Overview:

My research focuses on numerical methods for solving PDEs, fluid dynamics and uncertainty quantification applied to equations that are highly sensitive to model parameters. My interest is in developing computationally efficient schemes for solving certain flow problems, often oriented around data assimilation and analyzing the numerical convergence and stability. The papers I've worked on use an ensemble method that involves multiple realizations of parameters, such as initial conditions and forcing terms, applied to the MHD equations to develop high order schemes based in finite element methods (FEM). We've involved in some schemes The Scalar Auxiliary Variable method, a type of Lagrange multiplier technique for discretizing nonlinear terms explicitly that results in decoupled, unconditionally stable schemes with respect to a modified energy. Regularization techniques influenced by physical characteristics of the system, such as artificial viscosity regularization, are employed to enhance stability and in cases significantly improve long-time accuracy.