The divDiv complex: A construction based on the Bernstein-Gelfand-Gelfand resolution
ao.Univ.-Prof. Dipl.-Ing. Dr. Walter ZulehnerJan. 12, 2021, 2:30 p.m. ZOOM
The divDiv complex is a differential complex, which plays an important role in the analysis of biharmonic problems, problems in linear elasticity, and problems in general relativity. We will show how the divDiv complex can be constructively derived from four copies of the de Rham complex. Here we follow closely the article , where another differential complex, the elasticity complex, was derived from six copies of the de Rham complex. Based on this approach new finite element methods for linear elasticity were derived from known discretizations of the de Rham complex in . Similar results are expected for discretizations of problems related to the divDiv complex.
 D. N. Arnold, R. S. Falk and R. Winther. "Mixed finite element methods for linear elasticity with weakly imposed symmetry." Math. Comput., 76:1699–1723, 2007.