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Goal-Oriented Adaptivity and Multilevel Preconditioning for the Poisson-Boltzmann Equation
Burak Aksoylu, Stephen Bond, Eric Cyr +1
In this article, we develop goal-oriented error indicators to drive adaptive refinement algorithms for the Poisson-Boltzmann equation. Empirical results for the solvation free ener…
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…
Convergence of Goal-Oriented Adaptive Finite Element Methods for Nonsymmetric Problems
Michael Holst, Sara Pollock
In this article we develop convergence theory for a class of goal-oriented adaptive finite element algorithms for second order nonsymmetric linear elliptic equations. In particular…
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…