Abstract
A higher order finite volume method for elliptic problems is proposed for arbitrary order
. Piecewise polynomial basis functions are used as trial functions while the control volumes are constructed by a vertex-centered technique. The discretization is tested on numerical examples utilizing triangles and quadrilaterals in 2D. In these tests the optimal error is achieved in the
H
1
-norm. The error in the
L
2
-norm is one order below optimal for even polynomial degrees and optimal for odd degrees.