57 citations · 69 across the 14 of their papers we have counts for
15 papers
Stabilizer-Free Weak Galerkin Methods for Monotone Quasilinear Elliptic PDEs
Xiu Ye, Shangyou Zhang, Yunrong Zhu
In this paper, we study the stabilizer-free weak Galerkin methods on polytopal meshes for a class of second order elliptic boundary value problems of divergence form and with gradi…
Auxiliary space preconditioners for virtual element methods on polytopal meshes
Yunrong Zhu
In this paper, we develop the auxiliary space preconditioners for solving the linear system arising from the virtual element methods discretization on polytopal meshes for the seco…
A matrix analysis approach to discrete comparison principles for nonmonotone PDE
Sara Pollock, Yunrong Zhu
We consider a linear algebra approach to establishing a discrete comparison principle for a nonmonotone class of quasilinear elliptic partial differential equations. In the absence…
Discrete comparison principles for quasilinear elliptic PDE
Sara Pollock, Yunrong Zhu
Comparison principles are developed for discrete quasilinear elliptic partial differential equations. We consider the analysis of a class of nonmonotone Leray-Lions problems featur…
Multilevel Preconditioners for Reaction-Diffusion Problems with Discontinuous Coefficients
Tzanio V. Kolev, Jinchao Xu, Yunrong Zhu
In this paper, we extend some of the multilevel convergence results obtained by Xu and Zhu in [Xu and Zhu, M3AS 2008], to the case of second order linear reaction-diffusion equatio…
Convergence of Goal-Oriented Adaptive Finite Element Methods for Semilinear Problems
Michael Holst, Sara Pollock, Yunrong Zhu
In this article we develop a convergence theory for goal-oriented adaptive finite element algorithms designed for a class of second-order semilinear elliptic equations. We briefly…
Two-Grid Methods for Semilinear Interface Problems
Michael Holst, Ryan Szypowski, Yunrong Zhu
In this article we consider two-grid finite element methods for solving semilinear interface problems in d space dimensions, for d=2 or d=3. We first describe in some detail the ta…
Finite Element Exterior Calculus for Evolution Problems
Andrew Gillette, Michael Holst, Yunrong Zhu
Arnold, Falk, and Winther [Bull. Amer. Math. Soc. 47 (2010), 281--354] showed that mixed variational problems, and their numerical approximation by mixed methods, could be most com…
Analysis of a multigrid preconditioner for Crouzeix-Raviart discretization of elliptic PDE with jump coefficient
Yunrong Zhu
In this paper, we present a multigrid -cycle preconditioner for the linear system arising from piecewise linear nonconforming Crouzeix-Raviart discretization of second order ell…
Finite Element Error Estimates for Critical Growth Semilinear Problems without Angle Conditions
Randolph E. Bank, Michael Holst, Ryan Szypowski +1
In this article we consider a priori error and pointwise estimates for finite element approximations of solutions to semilinear elliptic boundary value problems in d>=2 space dimen…
Multigrid Preconditioner for Nonconforming Discretization of Elliptic Problems with Jump Coefficients
Blanca Ayuso De Dios, Michael Holst, Yunrong Zhu +1
In this paper, we present a multigrid preconditioner for solving the linear system arising from the piecewise linear nonconforming Crouzeix-Raviart discretization of second order e…
Adaptive Finite Element Methods with Inexact Solvers for the Nonlinear Poisson-Boltzmann Equation
Michael Holst, Ryan Szypowski, Yunrong Zhu
In this article we study adaptive finite element methods (AFEM) with inexact solvers for a class of semilinear elliptic interface problems. We are particularly interested in nonlin…
Multilevel Preconditioners for Discontinuous Galerkin Approximations of Elliptic Problems with Jump Coefficients
Blanca Ayuso De Dios, Michael Holst, Yunrong Zhu +1
We introduce and analyze two-level and multi-level preconditioners for a family of Interior Penalty (IP) discontinuous Galerkin (DG) discretizations of second order elliptic proble…
Adaptive Finite Element Modeling Techniques for the Poisson-Boltzmann Equation
Michael Holst, James Andrew McCammon, Zeyun Yu +2
We develop an efficient and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the regularization technique of Chen…
Local Multilevel Preconditioners for Elliptic Equations with Jump Coefficients on Bisection Grids
Long Chen, Michael Holst, Jinchao Xu +1
The goal of this paper is to design optimal multilevel solvers for the finite element approximation of second order linear elliptic problems with piecewise constant coefficients on…