Chapter 6 - Super-convergent patch recovery

Abstract

The super-convergent patch (SCP) recovery method is relativity easy to understand and is accurate for a wide range of problems. It was selected for implementation in the educational program MODEL. Its implementation is designed for use with most of the numerically integrated 1D, 2D, and 3D elements in the MODEL library. The SCP recovery process is clearly heuristic in nature, so some arbitrary choices need to be made in the implementation. This chapter defines a “patch” to be a local group of elements surrounding at least one interior node or being adjacent to a boundary node. The original research in SCP recovery methods used patches sequentially built around each node in the mesh. Later it was widely recognized that one could use a patch for every element in the mesh. Therefore, three types of patches are defined: node-based patch: an adjacent group of elements associated with a particular node; element-based patch: all elements adjacent to a particular element; face-based patch: this subset of the element-based patch includes only the adjacent elements that share a common face with the selected element. For 2D elements this means that they share a common edge. In MODEL the default is to use an element-based patch. However, one can investigate other options by utilizing some of the available control keywords. The whole basis of the SCP recovery is that there are special locations within an element where it can be shown that the derivatives are most accurate or exact for a given polynomial degree.