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dc.contributor.authorKraus, Johannes
dc.contributor.authorNakov, Svetoslav
dc.contributor.authorRepin, Sergey
dc.date.accessioned2020-06-09T11:11:49Z
dc.date.available2020-06-09T11:11:49Z
dc.date.issued2020
dc.identifier.citationKraus, J., Nakov, S., & Repin, S. (2020). Reliable Numerical Solution of a Class of Nonlinear Elliptic Problems Generated by the Poisson–Boltzmann Equation. <i>Computational Methods in Applied Mathematics</i>, <i>20</i>(2), 293-319. <a href="https://doi.org/10.1515/cmam-2018-0252" target="_blank">https://doi.org/10.1515/cmam-2018-0252</a>
dc.identifier.otherCONVID_30946703
dc.identifier.otherTUTKAID_81675
dc.identifier.urihttps://jyx.jyu.fi/handle/123456789/69799
dc.description.abstractWe 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.fi
dc.format.mimetypeapplication/pdf
dc.language.isoeng
dc.publisherWalter de Gruyter GmbH
dc.relation.ispartofseriesComputational Methods in Applied Mathematics
dc.rightsIn Copyright
dc.subject.otherPoisson-Boltzmann equation
dc.subject.othersemilinear partial differential equations
dc.subject.otherexistence and uniqueness of solutions
dc.subject.otherconvergence of finite element approximations
dc.subject.othera priori error estimates
dc.subject.otherguaranteed and efficient a posteriori error bounds
dc.subject.othererror indicators and adaptive mesh refinement
dc.titleReliable Numerical Solution of a Class of Nonlinear Elliptic Problems Generated by the Poisson–Boltzmann Equation
dc.typearticle
dc.identifier.urnURN:NBN:fi:jyu-202005273513
dc.contributor.laitosInformaatioteknologian tiedekuntafi
dc.contributor.laitosFaculty of Information Technologyen
dc.type.urihttp://purl.org/eprint/type/JournalArticle
dc.date.updated2020-05-27T09:15:11Z
dc.description.reviewstatuspeerReviewed
dc.format.pagerange293-319
dc.relation.issn1609-4840
dc.relation.numberinseries2
dc.relation.volume20
dc.type.versionsubmittedVersion
dc.rights.copyright© 2020 Walter de Gruyter GmbH, Berlin/Boston.
dc.rights.accesslevelopenAccessfi
dc.subject.ysodifferentiaaliyhtälöt
dc.format.contentfulltext
jyx.subject.urihttp://www.yso.fi/onto/yso/p3552
dc.rights.urlhttp://rightsstatements.org/page/InC/1.0/?language=en
dc.relation.doi10.1515/cmam-2018-0252


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