Efficient visualization of high-order finite elements

A general method for the post-processing treatment of high-order finite element fields is presented. The method applies to general polynomial fields, including discontinuous finite element fields. The technique uses error estimation and h-refinement to provide an optimal visualization grid. Some filtering is added to the algorithm in order to focus the refinement on a visualization plane or on the computation of one single iso-zero surface. 2D and 3D examples are provided that illustrate the power of the technique. In addition, schemes and algorithms that are discussed in the paper are readily available as part of an open source project that is developed by the authors, namely Gmsh.