2021/12/10 by Kamana Porwal, Porwal, Kamana, Pratibha Shakya +1
Computer Science · Engineering · #49J20 #49K20 #65N15 #65N30 #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2112.05389
openalex publication_date 2021/12/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article is concerned with the nonconforming finite element method for distributed elliptic optimal control problems with pointwise constraints on the control and gradient of the state variable. We reduce the minimization problem into a pure state constraint minimization problem. In this case, the solution of the minimization problem can be characterized as fourth-order elliptic variational inequalities of the first kind. To discretize the control problem we have used the bubble enriched Morley finite element method. To ensure the existence of the solution to discrete problems three bubble functions corresponding to the mean of the edge are added to the discrete space. We derive the error in the state variable in H2-type energy norm. Numerical results are presented to illustrate our analytical findings.