✍ Scribed by V. J. Ervin; E. P. Stephan; S. Abou El-Seoud
No coin nor oath required. For personal study only.
A weakly singular integral equation of the first kind on a plane surface piece Γ is solved approximately via the Galerkin method. The determination of the solution of this integral equation (with the single‐layer potential) is a classical problem in physics, since its solution represents the charge density of a thin, electrified plate Γ loaded with some given potential. Using piecewise constant or piecewise bilinear boundary elements we derive asymptotic estimates for the Galerkin error in the energy norm and analyse the effect of graded meshes. Estimates in lower order Sobolev norms are obtained via the Aubin–Nitsche trick. We describe in detail the numerical implementation of the Galerkin method with both piecewise‐constant and piecewise‐linear boundary elements. Numerical experiments show experimental rates of convergence that confirm our theoretical, asymptotic results.
📜 SIMILAR VOLUMES
## Abstract Understanding the complex interplay between the 3D structural hierarchy within thin films of conjugated polymers and the properties of devices based thereon is starting to be recognized as an important challenge in the continued development of these materials for a range of applications