Interpolation remainder theory from taylor expansions with non-rectangular domains of influence

Sobolev norm error bounds are derived for interpolation remainders on triangles using two types of Taylor expansion. These bounds are applied to the finite element analysis of Poisson's equation on a triangulation of a polygonal region

Smooth polynomial interpolation to boundary data on triangles

Boolean sum interpolation theory is used to derive a polynomial interpolant which interpolates a function F ∈ CN(∂T), and its derivatives of order N and less, on the boundary 3T of a triangle T. A triangle with one curved side is also considered

Compatable smooth interpolation in triangles

Boolean sum smooth interpolation to boundary data on a triangle is described. Sufficient conditions are given so that the functions when pieced together form a CN-1(Ω) function over a triangular subdivision of a polygonal region Ω and the precision sets of the interpolation functions are derived. The interpolants are modified so that the compatability conditions on the function which is interpolated can be removed and a C1 interpolant is used to illustrate the theory. The generation of interpolation schemes for discrete boundary data is also discussed