Coupling of nonconforming finite elements and boundary elements I: A priori estimates

Nonconforming finite element methods are sometimes considered as a variational crime and so we may regard its coupling with boundary element methods. In this paper, the symmetric coupling of nonconforming finite elements and boundary elements is established and a priori error estimates are shown. The coupling involves a further continuous layer on the interface in order to separate the nonconformity in the domain from its boundary data which are required to be continuous. Numerical examples prove the new scheme useful in practice. A posteriori error control and adaptive algorithms will be studied in the forthcoming Part II.