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
Publication in research information system
MetadataShow full item record
Showing items with similar title or keywords.
Liimatainen, Tony; Lin, Yi-Hsuan; Salo, Mikko; Tyni, Teemu (Elsevier, 2022)We study inverse problems for semilinear elliptic equations with fractional power type nonlinearities. Our arguments are based on the higher order linearization method, which helps us to solve inverse problems for certain ...
Nurminen, Janne (Elsevier, 2023)In this article we focus on inverse problems for a semilinear elliptic equation. We show that a potential q in ��/2+�, �>0, can be determined from the full and partial Dirichlet-to-Neumann map. This extends the results ...
Lassas, Matti; Liimatainen, Tony; Lin, Yi-Hsuan; Salo, Mikko (Elsevier, 2021)We introduce a method for solving Calderón type inverse problems for semilinear equations with power type nonlinearities. The method is based on higher order linearizations, and it allows one to solve inverse problems for ...
Matculevich, Svetlana (University of Jyväskylä, 2015)
Anjam, Immanuel; Pauly, Dirk (University of Jyväskylä, 2014)