Geodesic
On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains
Applications of Mathematics, Tome 46 (2001) no. 5, pp. 353-382.

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The paper is concerned with the study of an elliptic boundary value problem with a nonlinear Newton boundary condition considered in a two-dimensional nonpolygonal domain with a curved boundary. The existence and uniqueness of the solution of the continuous problem is a consequence of the monotone operator theory. The main attention is paid to the effect of the basic finite element variational crimes: approximation of the curved boundary by a polygonal one and the evaluation of integrals by numerical quadratures. With the aid of some important properties of Zlámal’s ideal triangulation and interpolation, the convergence of the method is analyzed.
DOI : 10.1023/A:1013756310753
Classification : 35J05, 35J65, 65N12, 65N15, 65N30
Keywords: elliptic equation; nonlinear Newton boundary condition; monotone operator method; finite element approximation; approximation of a curved boundary; numerical integration; ideal triangulation; ideal interpolation; convergence of the finite element method 
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     title = {On the finite element analysis of problems with nonlinear {Newton} boundary conditions in nonpolygonal domains},
     journal = {Applications of Mathematics},
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Feistauer, Miloslav; Najzar, Karel; Sobotíková, Veronika. On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains. Applications of Mathematics, Tome 46 (2001) no. 5, pp. 353-382. doi : 10.1023/A:1013756310753. http://geodesic.mathdoc.fr/articles/10.1023/A:1013756310753/

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