A note on polynomial approximation in Sobolev spaces
Error estimates for some quasi-interpolation operators
Mixed Finite Element Approximation of the Vector Potential.
Finite Element Approximation of Incompressible Navier-Stokes Equations with Slip Boundary Condition.
A note on polynomial approximation in Sobolev spaces
For domains which are star-shaped w.r.t. at least one point, we give new bounds on the constants in Jackson-inequalities in Sobolev spaces. For convex domains, these bounds do not depend on the eccentricity. For non-convex domains with a re-entrant corner, the bounds are uniform w.r.t. the exterior angle. The main tool is a new projection operator onto the space of polynomials.
Error estimates for some quasi-interpolation operators
We derive explicit bounds on the constants in error estimates for two quasi-interpolation operators which are modifications of the “classical” Clément-operator. These estimates are crucial for making explicit the constants which appear in popular error estimates. They are also compared with corresponding estimates for the standard nodal interpolation operator.
A posteriori error analysis of the fully discretized time-dependent Stokes equations
The time-dependent Stokes equations in two- or three-dimensional bounded domains are discretized by the backward Euler scheme in time and finite elements in space. The error of this discretization is bounded globally from above and locally from below by the sum of two types of computable error indicators, the first one being linked to the time discretization and the second one to the space discretization.
error analysis of the fully discretized time-dependent Stokes equations
The time-dependent Stokes equations in two- or three-dimensional bounded domains are discretized by the backward Euler scheme in time and finite elements in space. The error of this discretization is bounded globally from above and locally from below by the sum of two types of computable error indicators, the first one being linked to the time discretization and the second one to the space discretization.
A finite element discretization of the three-dimensional Navier–Stokes equations with mixed boundary conditions
We consider a variational formulation of the three-dimensional Navier–Stokes equations with mixed boundary conditions and prove that the variational problem admits a solution provided that the domain satisfies a suitable regularity assumption. Next, we propose a finite element discretization relying on the Galerkin method and establish and error estimates.
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