TREE-COTREE DECOMPOSITIONS FOR FIRST-ORDER COMPLETE TANGENTIAL VECTOR FINITE ELEMENTS

Edge-based Þnite elements have important applications in modelling both quasi-static and high-frequency electromagnetic problems. Recent work has demonstrated that formulations that exploit the graph structure of the edge-based Þnite element mesh may be extended to higher-order elements. This paper presents the details of how such an extension to a Þrst-order complete Þnite element is accomplished and illustrates its application in two-dimensional magnetostatics.