Preprint 2024-21
Tomás Barrios, Edwin Behrens, Rommel Bustinza:
On the approximation of the Lamé equations considering nonhomogeneous Dirichlet boundary condition: A new approach
Abstract:
We develop a numerical analysis for the linear elasticity problem with non homogeneous Dirichlet boundary condition, approximated by an unusual conforming finite element scheme. Specifically, for our approach, we show optimal rate of convergence for the a priori error analysis, which turns out to be valid for both 2D and 3D. In addition, we include an a posteriori error analysis based on the Ritz projection of the error, and we present an a posteriori error estimator that is reliable and local efficient. We remark that the resulting scheme has fewer degrees of freedom than many others for the same problem, that can be found in the current literature. We provide numerical experiments that illustrate the performance of the corresponding adaptive algorithm and support its use in practice.
