Adaptive Finite Element Methods with Inexact Solvers for the Nonlinear Poisson-Boltzmann Equation

  • Michael Holst
  • Ryan Szypowski
  • Yunrong Zhu
Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 91)


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 nonlinear problems with discontinuous diffusion coefficients, such as the nonlinear Poisson-Boltzmann equation and its regularizations. The algorithm we study consists of the standard SOLVE-ESTIMATE-MARK-REFINE procedure common to many adaptive finite element algorithms, but where the SOLVE step involves only a full solve on the coarsest level, and the remaining levels involve only single Newton updates to the previous approximate solution.


Convergence Plot Exact Solver Adaptive Finite Element Method Inexact Solution Standard Piecewise 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Departments of Mathematics and PhysicsUniversity of California San DiegoLa JollaUSA
  2. 2.Department of Mathematics and StatisticsCalifornia State Polytechnic University, PomonaPomonaUSA
  3. 3.Department of MathematicsIdaho State UniversityPocatelloUSA

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