9 citations · 10 across the 5 of their papers we have counts for
8 papers
Analysis of continuous data assimilation with large (or even infinite) nudging parameters
Amanda Diegel, Xuejian Li, Leo G. Rebholz
This paper considers continuous data assimilation (CDA) in partial differential equation (PDE) discretizations where nudging parameters can be taken arbitrarily large. We prove tha…
Convergence Analysis of a Preconditioned Steepest Descent Solver for the Cahn-Hilliard Equation with Logarithmic Potential
Amanda E. Diegel, Cheng Wang, Steven M. Wise
In this paper, we provide a theoretical analysis for a preconditioned steepest descent (PSD) iterative solver that improves the computational time of a finite difference numerical…
Continuous data assimilation and long-time accuracy in a interior penalty method for the Cahn-Hilliard equation
Amanda E. Diegel, Leo G. Rebholz
We propose a numerical approximation method for the Cahn-Hilliard equations that incorporates continuous data assimilation in order to achieve long time accuracy. The method uses a…
A C0 Interior Penalty Method for the Phase Field Crystal Equation
Amanda E. Diegel, Natasha Sharma
We present a C0 interior penalty finite element method for the sixth-order phase field crystal equation. We demonstrate that the numerical scheme is uniquely solvable, unconditiona…
A Finite Element Method for a Phase Field Model of Nematic Liquid Crystal Droplets
Amanda E. Diegel, Shawn W. Walker
We develop a novel finite element method for a phase field model of nematic liquid crystal droplets. The continuous model considers a free energy comprised of three components: the…
Convergence Analysis and Error Estimates for a Second Order Accurate Finite Element Method for the Cahn-Hilliard-Navier-Stokes System
Amanda E. Diegel, Cheng Wang, Xiaoming Wang +1
In this paper, we present a novel second order in time mixed finite element scheme for the Cahn-Hilliard-Navier-Stokes equations with matched densities. The scheme combines a stand…
Stability and Convergence of a Second Order Mixed Finite Element Method for the Cahn-Hilliard Equation
Amanda E. Diegel, Cheng Wang, Steven M. Wise
In this paper we devise and analyze an unconditionally stable, second-order-in-time numerical scheme for the Cahn-Hilliard equation in two and three space dimensions. We prove that…
Analysis of a Mixed Finite Element Method for a Cahn-Hilliard-Darcy-Stokes System
Amanda E. Diegel, Xiaobing H. Feng, Steven M. Wise
In this paper we devise and analyze a mixed finite element method for a modified Cahn-Hilliard equation coupled with a non-steady Darcy-Stokes flow that models phase separation and…