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dc.contributor.authorEfendiev, M. A. ( )
dc.contributor.authorSchmitz, H. ( )
dc.contributor.authorWendland, W. L. ( )
dc.date.accessioned2019-11-12T21:00:25Z
dc.date.available2019-11-12T21:00:25Z
dc.date.issued1999-05-28
dc.identifier.citationEfendiev, M., Schmitz, H., & Wendland, W. L. (1999). On some nonlinear potential problems. Electronic Journal of Differential Equations, 1999(18), pp. 1-17.en_US
dc.identifier.issn1072-6691
dc.identifier.urihttps://digital.library.txstate.edu/handle/10877/8798
dc.description.abstractThe degree theory of mappings is applied to a two-dimensional semilinear elliptic problem with the Laplacian as principal part subject to a nonlinear boundary condition of Robin type. Under some growth conditions we obtain existence. The analysis is based on an equivalent coupled system of domain--boundary variational equations whose principal parts are the Dirichlet bilinear form in the domain and the single layer potential bilinear form on the boundary, respectively. This system consists of a monotone and a compact part. Additional monotonicity implies convergence of an appropriate Richardson iteration. The degree theory also provides the instrument for showing convergence of a subsequence of a nonlinear finite element - boundary element Galerkin scheme with decreasing mesh width. Stronger assumptions provide strong monotonicity, uniqueness and convergence of the discrete Richardson iterations. Numerical experiments show that the Richardson parameter as well as the number of iterations (for given accuracy) are independent of the mesh width.en_US
dc.formatText
dc.format.extent17 pages
dc.format.medium1 file (.pdf)
dc.language.isoen_USen_US
dc.publisherTexas State University, Department of Mathematicsen_US
dc.sourceElectronic Journal of Differential Equations, 1999, San Marcos, Texas: Southwest Texas State University and University of North Texas.
dc.subjectNonlinear elliptic boundary value problemsen_US
dc.subjectDegree ofmappingsen_US
dc.subjectFinite elementen_US
dc.subjectBoundary element approximationen_US
dc.titleOn Some Nonlinear Potential Problemsen_US
txstate.documenttypeArticle
dc.rights.licenseCreative Commons Attribution 4.0 International License https://creativecommons.org/licenses/by/4.0/


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