4 papers
Explaining oscillatory behavior in convection-diffusion discretization
Constantin Bacuta
For a model convection-diffusion problem, we address the presence of oscillatory discrete solutions, and study difficulties in recovering standard approximation results for its sol…
On convergence of upwinding Petrov-Galerkin methods for convection-diffusion
Constantin Bacuta
We consider special upwinding Petrov-Galerkin discretizations for convection-diffusion problems. For the one dimensional case with a standard continuous linear element as the trial…
Connections Between Finite Difference and Finite Element Approximations
Cristina Bacuta, Constantin Bacuta
We present useful connections between the finite difference and the finite element methods for a model boundary value problem. We start from the observation that, in the finite ele…
Efficient discretization and preconditioning of the singularly perturbed Reaction Diffusion problem
Constantin Bacuta, Daniel Hayes, Jacob Jacavage
We consider the reaction diffusion problem and present efficient ways to discretize and precondition in the singular perturbed case when the reaction term dominates the equation. U…