Reliable Numerical Solution of a Class of Nonlinear Elliptic Problems Generated by the Poisson–Boltzmann Equation
Kraus, J., Nakov, S., & Repin, S. (2020). Reliable Numerical Solution of a Class of Nonlinear Elliptic Problems Generated by the Poisson–Boltzmann Equation. Computational Methods in Applied Mathematics, 20(2), 293-319. https://doi.org/10.1515/cmam-2018-0252
Published inComputational Methods in Applied Mathematics
© 2020 Walter de Gruyter GmbH, Berlin/Boston.
We consider a class of nonlinear elliptic problems associated with models in biophysics, which are described by the Poisson–Boltzmann equation (PBE). We prove mathematical correctness of the problem, study a suitable class of approximations, and deduce guaranteed and fully computable bounds of approximation errors. The latter goal is achieved by means of the approach suggested in  for convex variational problems. Moreover, we establish the error identity, which defines the error measure natural for the considered class of problems and show that it yields computable majorants and minorants of the global error as well as indicators of local errors that provide efficient adaptation of meshes. Theoretical results are confirmed by a collection of numerical tests that includes problems on 2D and 3D Lipschitz domains.
PublisherWalter de Gruyter GmbH
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