No abstract

We introduce and investigate the modified TV-Stokes model for two classical image processing tasks, i.e., image restoration and image inpainting. The modified TV-Stokes model is a two-step model based on a total variation (TV) minimization in each step and the use of geometric information of the image. In the first step, a smoothed and divergence free tangential field of the given image is recovered, and in the second step, the image is reconstructed from the corresponding normals. The existence and the uniqueness of the solution to the minimization problems are established for both steps of the model. Numerical examples and comparisons are presented to illustrate the effectiveness of the model.

No abstract

The problem of stationary flow of a nonlinearly viscous fluid is studied under the “velocity‐pressure” mixed formulation, the surface forces are prescribed on one portion of the boundary and the velocities are given on the other portion. The problem is considered under Stokes approximation, i.e., the inertia forces are neglected. Existence and uniqueness are proved, and finite element approximation for velocity and pressure as well as iterative methods are studied.

No abstract