Finite Element Convergence for Singular Data.
Sobolev type inequalities for p>0
Finite-element discretizations of a two-dimensional grade-two fluid model
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...
Finite-element discretizations of a two-dimensional grade-two fluid model
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...
A family of finite elements with optimal approximation properties for various Galerkin methods for 2nd and 4th order problems
Regular inversion of the divergence operator with Dirichlet boundary conditions on a polygon
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