A POSTERIORI ANALYSIS AND EFFICIENT REFINEMENT STRATEGIES FOR THE POISSON-BOLTZMANN EQUATION

作者：Chaudhry Jehanzeb H^*

来源：SIAM Journal on Scientific Computing, 2018, 40(4): A2519-A2542.

DOI：10.1137/17M1119846

• a posteriori error estimation
• adjoint operator
• Poisson-Boltzmann equation
• finite element method
• mesh refinement

The Poisson-Boltzmann equation (PBE) models the electrostatic interactions of charged bodies such as molecules and proteins in an electrolyte solvent. The PBE is a challenging equation to solve numerically due to the presence of singularities, discontinuous coefficients, and boundary conditions. Hence, there is often large error in the numerical solution of the PBE that needs to be quantified. In this work, we use adjoint-based a posteriori analysis to accurately quantify the error in an important quantity of interest, the solvation free energy, for the finite element solution of the PBE. We identify various sources of error and propose novel refinement strategies based on a posteriori error estimates.

• 出版日期2018