Long Chen
Convergence and Optimality of Adaptive Mixed Finite Element Methods.
Tue, 01/12/2010 - 16:01 — SomNambulAuthors: Michael Holst, Long Chen, Jinchao Xu
Subjects: Numerical Analysis
AbstractThe convergence and optimality of adaptive mixed finite element methods for
the Poisson equation are established in this paper. The main difficulty for
mixed finite element methods is the lack of minimization principle and thus the
failure of orthogonality. A quasi-orthogonality property is proved using the
fact that the error is orthogonal to the divergence free subspace, while the
part of the error that is not divergence free can be bounded by the data
oscillation using a discrete stability result.The Finite Element Approximation of the Nonlinear Poisson-Boltzmann Equation.
Tue, 01/12/2010 - 16:01 — SomNambulAuthors: Michael Holst, Long Chen, Jinchao Xu
Subjects: Numerical Analysis
AbstractA widely used electrostatics model in the biomolecular modeling community,
the nonlinear Poisson-Boltzmann equation, along with its finite element
approximation, are analyzed in this paper. A regularized Poisson-Boltzmann
equation is introduced as an auxiliary problem, making it possible to study the
original nonlinear equation with delta distribution sources. A priori error
estimates for the finite element approximation are obtained for the regularized
Poisson-Boltzmann equation based on certain quasi-uniform grids in two and
three dimensions.
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