On the assembly of degenerate quadrilaterals in finite element methods

Abstract

Several problems in Physics and related fields yields to the necessity of solving elliptic problems on arbitrary domains. For instance, this kind of problems appears in potential theory, hydrodinamics and elasticity. Finite Element Method (F.E.M.) has proved to be a very useful tool to solve them numerically, in particular, when the aomain of the problem is not geometrically simple. (For a good descriptiin of the applications of F.E.M. to Mathematical Physics see II and references therein). As it is well known, the starting point of F.E.M. is the subdivision of the domain into elementary subdomains; v.g. quadrilaterals or triangles for plane domains.