arXiv subjects
Publications and source records attributed to Susanne C. Brenner.
We consider a model Poisson problem in $\R^d$ ($d=2,3$) and establish error estimates for virtual element methods on polygonal or polyhedral meshes that can contain small edges ($d=2$) or small faces ($d=3$).
We develop a robust solver for a mixed finite element convex splitting scheme for the Cahn-Hilliard equation. The key ingredient of the solver is a preconditioned minimal residual algorithm (with a multigrid preconditioner) whose performance is independent of the spacial mesh size and the time step size for a given interfacial width parameter. The dependence on the interfacial width parameter is also mild.
We design and analyze multigrid methods for the saddle point problems resulting from Raviart-Thomas-Nédélec mixed finite element methods (of order at least 1) for the Darcy system in porous media flow. Uniform convergence of the $W$-cycle algorithm in a nonstandard energy norm is established. Extensions to general second order elliptic problems are also addressed.
We develop an a posteriori analysis of C^0 interior penalty methods for the displacement obstacle problem of clamped Kirchhoff plates. We show that a residual based error estimator originally designed for C^0 interior penalty methods for the boundary value problem of clamped Kirchhoff plates can also be used for the obstacle problem. We obtain reliability and efficiency estimates for the error estimator and introduce an adaptive algorithm based on this error estimator. Numerical results indicate that the performance of the adaptive algorithm is optimal for both quadratic and cubic C^0 interior penalty methods.
A generalized finite element method for the displacement obstacle problem of clamped Kirchhoff plates is considered in this paper. We derive optimal error estimates and present numerical results that illustrate the performance of the method.
Discontinuous Petrov-Galerkin (DPG) methods are new discontinuous Galerkin methods with interesting properties. In this article we consider a domain decomposition preconditioner for a DPG method for the Poisson problem.