109 citations · 289 across the 56 of their papers we have counts for
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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…
Analysis of interior penalty discontinuous Galerkin methods for the Allen-Cahn equation and the mean curvature flow
Xiaobing Feng, Yukun Li
This paper develops and analyzes two fully discrete interior penalty discontinuous Galerkin (IP-DG) methods for the Allen-Cahn equation, which is a nonlinear singular perturbation…
On Schwarz Methods for Nonsymmetric and Indefinite Problems
Xiaobing Feng, Cody Lorton
In this paper we introduce a new Schwarz framework and theory, based on the well-known idea of space decomposition, for nonsymmetric and indefinite linear systems arising from cont…
Discontinuous Galerkin finite element differential calculus and applications to numerical solutions of linear and nonlinear partial differential equations
Xiaobing Feng, Thomas Lewis, Michael Neilan
This paper develops a discontinuous Galerkin (DG) finite element differential calculus theory for approximating weak derivatives of Sobolev functions and piecewise Sobolev function…