Mollified finite element approximants of arbitrary order and smoothness

The approximation properties of the finite element method can often be substantially improved by choosing smooth high-order basis functions. It is extremely difficult to devise such functions for partitions consisting arbitrarily shaped polytopes. We propose mollified arbitrary order and smoothness convex On each polytope an independent local polynomial approximant assumed. are defined as convolutions approximants with a mollifier. mollifier chosen smooth, have compact support unit volume. obtained governed smoothness. convolution integrals evaluated numerically first computing boolean intersection between then applying divergence theorem reduce dimension integrals. function given Minkowski sum respective breakpoints functions, i.e. locations non-infinite smoothness, not necessarily aligned boundaries. Furthermore, boundary interpolating so that we apply conditions non-symmetric Nitsche in immersed/embedded elements. presented numerical examples confirm optimal convergence proposed scheme Poisson elasticity problems.