Finite element compensators for thermo-elastic systems with boundary control and point observation
We consider a thermo-elastic plate equation on a bounded domain Ω, subject to a boundary control as a 'bending moment', and with point observation in the interior of Ω. The free dynamics generates a s.c. analytic semigroup on the natural energy space. Both control operator and observation operator are fully unbounded, with a combined degree of unboundedness > 1, the super-critical case. We construct an approximation theory, based on FEM, which leads to a finite-dimensional dynamic compensator, possessing all the expected desirable properties, once it is inserted into the original continuous system. In particular, it preserves the same margin of stability of the continuous problem, except, perhaps, for an arbitrary ε > 0.
Numerical Functional Analysis and Optimization
Chang, S., Lasiecka, I., & Triggiani, R. (1999). Finite element compensators for thermo-elastic systems with boundary control and point observation. Numerical Functional Analysis and Optimization, 20 (5-6), 419-435. https://doi.org/10.1080/01630569908816903