On the numerical analysis of finite element and Dirichlet-to-Neumann methods for nonlinear exterior transmission problems

Gabriel R. Barrenechea, Mauricio A. Barrientos, Gabriel N. Gatica

Resultado de la investigación: Contribución a una revistaArtículorevisión exhaustiva

2 Citas (Scopus)

Resumen

We provide the numerical analysis of the combination of finite elements and Dirichlet-to-Neumann mappings (based on boundary integral operators) for a class of nonlinear exterior transmission problems whose weak formulations reduce to Lipschitz-continuous and strongly monotone operator equations. As a model we consider a nonlinear second order elliptic equation in divergence form in a bounded inner region of the plane, coupled with the Laplace equation in the corresponding unbounded exterior part. A discrete Galerkin scheme is presented by using linear finite elements on a triangulation of the domain, and then applying numerical quadrature and analytical formulae to evaluate all the linear, bilinear and semilinear forms involved. We prove the unique solvability of the discrete equations, and show the strong convergence of the approximate solutions. Furthermore, assuming additional regularity on the solution of the continuous operator equation, the asymptotic rate of convergence O(h) is also derived. Finally, numerical experiments are presented, which confirm the convergence results.

Idioma originalInglés
Páginas (desde-hasta)705-735
Número de páginas31
PublicaciónNumerical Functional Analysis and Optimization
Volumen19
N.º7-8
DOI
EstadoPublicada - 1998
Publicado de forma externa

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