Curved Elements in the Finite Element Method. I

Abstract

Curved elements, introduced by the author in [13] and [14], which are suitable for solving boundary value problems of the second order in plane domains with an arbitrary boundary are discussed. An approximation theorem is proved, the Dirichlet problem for a ${\mathop W\limits^{\circ}} _2^{(1)} $-elliptic equation is considered as a model problem and error bounds are derived.