The divDiv complex: A construction based on the Bernstein-Gelfand-Gelfand resolution

ao.Univ.-Prof. Dipl.-Ing. Dr. Walter Zulehner

Jan. 12, 2021, 3:30 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
[1], 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 [1]. Similar results are expected for discretizations of problems related to the
divDiv complex.
[1] 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.