An a posteriori error estimator for the C0 Interior Penalty Approximations of Fourth Order Elliptic Boundary Value Problem on Quadrilateral Meshes
Numerical solutions of fourth order elliptic problems with finite element methods has been the topic of research in computational mechanics for over 50 years. Traditional approaches to solve these problems include using C1 conforming finite element methods which demand the C1 continuity of the underlying shape functions, which is computationally very expensive. In this work, we will present the C0 Interior Penalty Galerkin approximation of the fourth order elliptic problems which relies only on continuous i.e., C0 shape functions, which is much cheaper to implement. The spatial discretization is based on quadrilateral meshes and the underlying C0 shape functions are of degree at most 2. We are using the a residual-based a posteriori error estimator, for our a posteriori error analysis, and also we show and prove its reliability. We then used some benchmark problems in our numerical result section which illustrated the performance of the estimator.^
Rahman, Mohammad Arifur, "An a posteriori error estimator for the C0 Interior Penalty Approximations of Fourth Order Elliptic Boundary Value Problem on Quadrilateral Meshes" (2016). ETD Collection for University of Texas, El Paso. AAI10151260.