Colloquium: A posteriori analysis for the Poisson Boltzmann Equation
Thursday, November 16, 2017 -
3:30pm to 4:30pm
Abstract: 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 talk, 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. I will also briefly review my recent work on uncertainty quantification for elliptic problems on stochastic domains, a posteriori analysis for IMEX schemes and reduced basis methods for least-squares finite elements.
Contact Name: Jehanzeb Chaudhry