Higher Order Finite Elements on Sparse Grids

We present a general technique to construct hierarchical bases of higher order suitable for sparse grid methods without increasing the number of degrees of freedom. For the solution of elliptic partial differential equations, this approach allows us to profit both from the efficiency of sparse grid discretizations and from the advantages of higher order basis functions with regard to their approximation accuracy. We report the results of some first numerical experiments concerning piecewise biquadratic hierarchical basis functions.     «

We present a general technique to construct hierarchical bases of higher order suitable for sparse grid methods without increasing the number of degrees of freedom. For the solution of elliptic partial differential equations, this approach allows us to profit both from the efficiency of sparse grid discretizations and from the advantages of higher order basis functions with regard to their approximation accuracy. We report the results of some first numerical experiments concerning piecewise biqu...     »