Volume 22, Issue 3

- In this paper, we deal with the discontinuous Galerkin finite element method for the plate contact problem with the frictional boundary conditions. The weak formulation is the variational inequality problem of the second kind. In virtue of the special discrete variational formulation, the error estimate in the broken H 2 norm is derived between the discontinuous approximation solution and the exact solution.

- In this contribution, we show a method for the boundary feedback stabilization of the Stokes problem around a stationary trajectory. We derive a formal low-rank algorithm for solving the stabilization problem in operator notation. The appearing operator equations are formulated in terms of stationary partial differential equations (PDEs) instead of using their finite dimensional representations in terms of matrices. A Galerkin method, satisfying the divergence constraint pointwise locally is especially appealing since it represents appropriately the action of the Helmholtz projection. The main advantages of the composite technique are the efficient assembly of element matrices, the reduction of computational costs using static condensation, and the diagonal mass matrix. The non-conforming character of the composite element guarantees a better sparsity pattern, compared to conforming elements, due to the lower number of couplings between basis functions corresponding to neighboring cells. We also achieve the pointwise mass conservation on sub-triangles of each element.

- We prove global convergence of an inexact extended polyhedral Gauß-Seidel method for the minimization of strictly convex functionals that are continuously differentiable on each polyhedron of a polyhedral decomposition of their domains of definition. While pure Gauß-Seidel methods are known to be very slow for problems governed by partial differential equations, the presented convergence result also covers multilevel methods that extend the Gauß-Seidel step by coarse level corrections. Our result generalizes the proof of [10] for differentiable functionals on the Gibbs simplex. Example applications are given that require the generality of our approach.

- Suppose that the matrix equation AXB = C with unknown matrix X is given, where A, B, and C are known matrices of suitable size. The matrix nearness problem is considered over the (P,Q)-orthogonal symmetric and (P,Q)-orthogonal skew-symmetric solutions of the matrix equation AXB=C. The explicit forms of the best approximate solutions of the problems considered are established. Moreover, two numerical examples and a comparative table, depending on the examples chosen from literature, are given.