9 citations · 19 across the 14 of their papers we have counts for
16 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…
Comparison of variational discretizations for a convection-diffusion problem
Constantin Bacuta, Cristina Bacuta, Daniel Hayes
For a model convection-diffusion problem, we obtain new error estimates for a general upwinding finite element discretization based on bubble modification of the test space. The ke…
Connections Between Finite Difference and Finite Element Approximations for a Convection-Diffusion Problem
Constantin Bacuta, Cristina Bacuta
We consider a model convection-diffusion problem and present useful connections between the finite differences and finite element discretization methods. We introduce a general upw…
Results on a Mixed Finite Element Approach for a Model Convection-Diffusion Problem
Constantin Bacuta, Daniel Hayes, Tyler O'Grady
We consider a model convection-diffusion problem and present our recent numerical and analysis results regarding mixed finite element formulation and discretization in the singular…
Notes on Finite Element Discretization for a Model Convection-Diffusion Problem
Constantin Bacuta, Daniel Hayes, Tyler O'Grady
We present recent finite element numerical results on a model convection-diffusion problem in the singular perturbed case when the convection term dominates the problem. We compare…
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…
A nonconforming saddle point least squares approach for elliptic interface problems
Constantin Bacuta, Jacob Jacavage
We present a non-conforming least squares method for approximating solutions of second order elliptic problems with discontinuous coefficients. The method is based on a general Sad…
Saddle Point Least Squares Preconditioning of Mixed Methods
Constantin Bacuta, Jacob Jacavage
We present a simple way to discretize and precondition mixed variational formulations. Our theory connects with, and takes advantage of, the classical theory of symmetric saddle po…
Differential operators on domains with conical points: precise uniform regularity estimates
Constantin Bacuta, Hengguang Li, Victor Nistor
We study families of strongly elliptic, second order differential operators with singular coefficients on domains with conical points. We obtain uniform estimates on their inverses…
A note on stability and optimal approximation estimates for symmetric saddle point systems
Constantin Bacuta
We establish sharp well-posedness and approximation estimates for variational saddle point systems at the continuous level. The main results of this note have been known to be true…
Boundary integral solvers for an evolutionary exterior Stokes problem
Constantin Bacuta, Matthew E. Hassell, George C. Hsiao +1
This paper proposes and analyzes a full discretization of the exterior transient Stokes problem with Dirichlet boundary conditions. The method is based on a single layer boundary i…
Cascadic Multilevel Algorithms for Symmetric Saddle Point Systems
Constantin Bacuta
In this paper, we introduce a multilevel algorithm for approximating variational formulations of symmetric saddle point systems. The algorithm is based on availability of families…
Anisotropic regularity and optimal rates of convergence for the Finite Element Method on three dimensional polyhedral domains
Constantin Bacuta, Anna L. Mazzucato, Victor Nistor
We consider the model Poisson problem , on $\pa Ω$, where is a bounded polyhedral domain in $\RR^n$. The objective of the paper is twofold. The first ob…
Regularity and well posedness for the Laplace operator on polyhedral domains
Constantin Bacuta, Victor Nistor, Ludmil Zikatanov
We announce a well-posedness result for the Laplace equation in weighted Sobolev spaces on polyhedral domains in $\RR^n$ with Dirichlet boundary conditions. The weight is the dista…