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On the Finite Element Analysis of Problems with Nonlinear Newton Boundary Conditions in Nonpolygonal Domains |
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| Authors: | Miloslav Feistauer Karel Najzar Veronika Sobotikova |
| Institution: | (1) Institute of Numerical Mathematics, Faculty of Mathematics and Physics, Charles University, Sokolovska 83, 186 75 Praha 8, Czech Republic;(2) Department of Mathematics, Faculty of Electrical Engineering, Czech Technical University, Technicka 2, 166 27 Praha 6, Czech Republic sobotik@math.feld.cvut.cz |
| Abstract: | 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 Zlamal's ideal triangulation and interpolation, the convergence of the method is analyzed. |
| 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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