Data-dependent triangulations for scattered data interpolation and finite element approximation (Q1802648)

The authors study two approximation schemes: interpolation of scattered data and finite element approximation to solutions of elliptic partial differential equations, to approximate a bivariate function \(F(x,y)\), defined over some region \(A\), by a member of a finite-dimensional space of functions. They restrict their study to approximation methods in which the approximant is constructed over a triangulation of \(A\) and to the case where the approximant is a continuous piecewise linear polynomial. Several examples are given.