Mixed finite element method for a degenerate convex variational problem from topology optimization (Q2903000)

The paper is devoted to a mixed finite element method for degenerate convex variational problems in the spirit of topology optimization -- that is an active area of research. The authors start with an optimal design problem and continue with dual functional and Yosida regularization. The paper studies a mixed formulation together with discretizations, providing sufficient motivation for fixed formulation. All propositions and theorems are followed by step by step proofs, sharp techniques and are primarily based upon methods of convex minimization problems, functional analytic techniques especially for \(L^2\) and \(H^1\) Sobolev spaces and nice analytic inequalities (especially Cauchy-Schwarz). Numerical evidence supports the theoretical results of the present paper. The paper concludes with optimal design on a variety of domains.