A Mixed Finite Element Method for Coupled Plates

This paper introduces a mixed finite element method for the problem of two coupled plates with mixed boundary conditions and rigid junction conditions. By introducing the union of stresses and moments as an independent variable, which is of significant interest in practical applications, a mixed formulation is developed and its well-posedness is established. To avoid complications with the direct use of trace operators, the theory of densely defined operators in Hilbert spaces is employed to determine a suitable space that incorporates boundary and junction conditions for this variable. Based on the mixed formulation, a mixed finite element method is presented along with an illustrative example. The discrete stability and the a priori analysis for the mixed finite element method are proved under some assumptions. Numerical tests demonstrate the theoretical results.