Bourlard, Maryse; Nicaise, Serge; Paquet, Luc Deux méthodes d’éléments finis frontières raffinés pour la résolution du problème de Neumann dans un polygone. (Two adapted boundary element methods for the solution of the Neumann problem in a polygonal domain). (French) Zbl 0624.65118 C. R. Acad. Sci., Paris, Sér. I 305, 311-314 (1987). The solution of the Neumann problem in a plane domain with a polygonal boundary \(\Gamma\) is expressed either as the double layer potential of a function \(\phi\), which is the solution of a coercive variational problem on \(H^{1/2}(\Gamma)/{\mathbb{C}}\), or as the simple layer potential of the charge q, which is the solution of a Fredholm integral equation of the second kind on \(\Gamma\). We adapt the mesh near the corners in order to get rid of the polluting effect of the singularities on the order of convergence. Cited in 1 Document MSC: 65N35 Spectral, collocation and related methods for boundary value problems involving PDEs 65R20 Numerical methods for integral equations 35J20 Variational methods for second-order elliptic equations 35C15 Integral representations of solutions to PDEs 45E10 Integral equations of the convolution type (Abel, Picard, Toeplitz and Wiener-Hopf type) Keywords:adapted boundary element methods; polygonal domain; Neumann problem; double layer potential; coercive variational problem; simple layer potential; Fredholm integral equation of the second kind; singularities; order of convergence PDFBibTeX XMLCite \textit{M. Bourlard} et al., C. R. Acad. Sci., Paris, Sér. I 305, 311--314 (1987; Zbl 0624.65118)