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This paper is concerned with the finite volume approximation of the p-Laplacian equation with homogeneous Dirichlet boundary conditions on rectangular meshes.
A reconstruction of the norm of the gradient on the mesh's interfaces is needed in order to discretize the p-Laplacian operator. We give a detailed description of the possible nine points schemes ensuring that the solution of the resulting finite dimensional nonlinear system exists and is unique. These schemes, called admissible, are locally...
We propose and analyze several finite-element schemes for solving a grade-two fluid model, with a tangential boundary condition, in a two-dimensional polygon. The exact problem is split into a generalized Stokes problem and a transport equation, in such a way that it always has a solution without restriction on the shape of the domain and on the size of the data. The first scheme uses divergence-free discrete velocities and a centered discretization of the transport term, whereas the other schemes...
We propose and analyze several finite-element schemes for solving a grade-two
fluid model, with a
tangential boundary condition, in a two-dimensional polygon. The exact
problem is split into a
generalized Stokes problem and a transport equation, in such a way that it
always has a solution
without restriction on the shape of the domain and on the size of the data.
The first scheme uses
divergence-free discrete velocities and a centered discretization of the
transport term, whereas the
other schemes...
We propose and analyse a abstract framework for augmented mixed formulations.
We give a priori error estimate in the general case: conforming and
nonconforming approximations with or without numerical integration.
Finally, a posteriori error estimator is given. An example of stabilized
formulation for Stokes problem is analysed.
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