We study finite element methods for the displacement obstacle problem of clamped Kirchhoff plates. A unified convergence analysis is provided for C1 finite element methods, classical nonconforming finite element methods and C0 interior penalty methods. Under the condition that the obstacles are sufficiently smooth and that they are separated from each other and the zero displacement boundary co...

The approximate solution of optimization and control problems for systems governed by linear, elliptic partial differential equations is considered. Such problems are most often solved using methods based on the application of the Lagrange multiplier rule followed by discretization through, e.g., a Galerkin finite element method. As an alternative, we show how least-squares finite element metho...

The occurrence of spurious solutions is a well-known limitation of the standard nodal finite element method when applied to electromagnetic problems. The two commonly used remedies that are used to address this problem are (i) The addition of a penalty term with the penalty factor based on the local dielectric constant, and which reduces to a Helmholtz form on homogeneous domains (regularized f...

In this article, we first consider some penalized finite element methods for the stationary Navier-stokes equations, based on the finite element space pair (Xh, Mh) which satisfies the discrete inf-sup condition for the P2−P0 element or does not satisfy the discrete inf-sup condition for the P1−P0 element. Then, we consider two-level penalty finite element methods which involve solving one smal...

We consider an interior penalty discontinuous approximation for symmetric elliptic problems of second order on non–matching grids in this paer. The main result is an almost optimal error estimate for the interior penalty approximation of the original problem based on the partition of the domain into a finite number of subdomains. Further, an error analysis for the finite element approximation o...

This paper studies the application of an inverse methodology for problem solving in fracture mechanics using the finite element analysis. The method was applied to both detection of subsurface cracks and the study of propagating cracks. The procedure for detection of subsurface cracks uses a first order optimization analysis coupled with a penalty function to solve for the unknown geometric par...

We investigate the C interior penalty Galerkin (C IPG) method for biharmonic eigenvalue problems with the boundary conditions of the clamped plate, the simply supported plate and the Cahn-Hilliard type. We prove the convergence of the method and present numerical results to illustrate its performance. We also compare the C IPG method with the Argyris C finite element method, the Ciarlet-Raviart...