A mixed formulation with two main variables, based on the Ciarlet-Raviart technique, with 0 C continuity shape functions is employed for the solution of some types of biharmonic equations in 1-D. The continuous and discrete Babuška-Brezzi inf-sup conditions are established. The formulation is numerically tested for both the hand pextensions. The model problems involve the standard biharmonic eq...

Recently the biharmonic form of the Navier-Stokes (N-S) equations have been solved in various domains by using second order compact discretization. In this paper, we present a fourth order essentially compact (4OEC) finite difference scheme for the steady N-S equations in geometries beyond rectangular. As a further advancement to the earlier formulations on the classical biharmonic equation tha...

We give a characterization of functions that are uniformly approximable on a compact subset K of R by biharmonic functions in neighborhoods of K.

We give a differential geometric interpretation for the classification of biharmonic curves in semi-Euclidean 3-space due to Chen and Ishikawa (1991).

A Fredholm second kind integral equation (SKIE) formulation is constructed for the Dirichlet problem of the biharmonic equation in three dimensions. A fast numerical algorithm is developed based on the constructed SKIE. Its performance is illustrated via several numerical examples.

We obtain some classification results and the stability conditions of nonminimal biharmonic anti-invariant submanifolds in Sasakian space forms. MSC 2000: 53C42 (primary); 53B25 (secondary)