ADAPTIVE FINITE ELEMENT MODELING TECHNIQUES FOR THE POISSON-BOLTZMANN EQUATION.

@article{Holst2012ADAPTIVEFE,
  title={ADAPTIVE FINITE ELEMENT MODELING TECHNIQUES FOR THE POISSON-BOLTZMANN EQUATION.},
  author={Michael J. Holst and James Andrew McCammon and Zeyun Yu and Youngcheng Zhou and Yunrong Zhu},
  journal={Communications in computational physics},
  year={2012},
  volume={11 1},
  pages={
          179-214
        }
}
  • Michael J. Holst, James Andrew McCammon, +2 authors Yunrong Zhu
  • Published in
    Communications in…
    2012
  • Mathematics, Computer Science, Physics, Medicine
  • We consider the design of an effective and reliable adaptive finite element method (AFEM) for the nonlinear Poisson-Boltzmann equation (PBE). We first examine the two-term regularization technique for the continuous problem recently proposed by Chen, Holst, and Xu based on the removal of the singular electrostatic potential inside biomolecules; this technique made possible the development of the first complete solution and approximation theory for the Poisson-Boltzmann equation, the first… CONTINUE READING

    Citations

    Publications citing this paper.
    SHOWING 1-10 OF 34 CITATIONS

    A Posteriori Analysis and Efficient Refinement Strategies for the Poisson-Boltzmann Equation

    VIEW 8 EXCERPTS
    CITES METHODS & BACKGROUND
    HIGHLY INFLUENCED

    On developing stable finite element methods for pseudo-time simulation of biomolecular electrostatics

    VIEW 4 EXCERPTS
    CITES METHODS & BACKGROUND
    HIGHLY INFLUENCED

    A two-component Matched Interface and Boundary (MIB) regularization for charge singularity in implicit solvation

    VIEW 7 EXCERPTS
    CITES BACKGROUND & METHODS
    HIGHLY INFLUENCED

    Convergence of goal-oriented adaptive finite element methods for semilinear problems

    VIEW 4 EXCERPTS
    CITES METHODS & BACKGROUND

    Goal-Oriented Adaptivity and Multilevel Preconditioning for the Poisson-Boltzmann Equation

    VIEW 9 EXCERPTS
    CITES METHODS & BACKGROUND

    A Domain Decomposition Method for the Poisson-Boltzmann Solvation Models

    VIEW 1 EXCERPT
    CITES BACKGROUND

    References

    Publications referenced by this paper.
    SHOWING 1-10 OF 64 REFERENCES

    The Finite Element Approximation of the Nonlinear Poisson-Boltzmann Equation

    VIEW 9 EXCERPTS

    Treatment of charge singularities in implicit solvent models.

    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    Convergence of Adaptive Finite Element Methods for General Second Order Linear Elliptic PDEs

    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    A Gaussian Description of Molecular Shape

    VIEW 4 EXCERPTS
    HIGHLY INFLUENTIAL

    Sobolev Spaces

    VIEW 1 EXCERPT