Abstract
In the first part of this paper we study in detail the properties of the divergence operator acting on continuous piecewise polynomials on some fixed triangulation; more specifically, we characterize the range and prove the existence of a maximal right-inverse whose norm grows at most algebraically with the degree of the piecewise polynomials. In the last part of this paper we apply these results to thep-version of the Finite Element Method for a nearly incompressible material with homogeneous Dirichlet boundary conditions. We show that thep-version maintains optimal convergence rates in the limit as the Poisson ratio approaches 1/2. This fact eliminates the need for any "reduced integration" such as customarily used in connection with the more standardh-version of the Finite Element Method.
Published Version
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