This thesis consists of two topics on discontinuous Galerkin (DG) finite element methods for time-dependent problems. In the first part of the thesis, we analyze …
Fractional-order partial differential equations (FPDEs) describe macroscopic properties of systems driven by Levy processes and, more generally, Continuous-Time Random Walks (CTRWs). CTRWs form a versatile …
The problem of forming exact sequences of finite element spaces that discretize Hilbert complexes is central to the finite element exterior calculus. This framework offers …
Many scientific simulations rely on the solution of very large linear systems of equations, and multigrid and domain decomposition methods are widely used solvers. It …
This dissertation is composed around the subject of multiscale modeling of soft matter and biophysical systems with applications using large-scale computations. Specifically, it is expanded …
The positivity-preserving property is a highly desirable property when designing high order numerical methods for hyperbolic conservation laws, since negative values sometimes cause ill-posedness of …