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Article

Feistauer, Miloslav ; Najzar, Karel ; Sobotíková, Veronika
On the finite element analysis of problems with nonlinear Newton boundary conditions in nonpolygonal domains. (English). Applications of Mathematics, vol. 46 (2001), issue 5, pp. 353-382
MSC: 35J05, 35J65, 65N12, 65N15, 65N30 | MR 1925193 | Zbl 1066.65124 | DOI: 10.1023/A:1013756310753
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
Summary:
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.
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