| Author | Carlos Rivas, Paul Barbone, Assad Oberai |
|---|---|
| Title | An augmented Lagrangian stabilized B-splines FEM formulation for the solution of an inverse elasticity problem |
| Year | 2012 |
| Journal | CMAME |
| Volume | to appear |
| Abstract | We consider an inverse problem in linear elastostatics formulated as a constrained optimization problem. We demonstrate well-posedness of the linearized saddle-point problem when the displacements are given in H2, and modulus field in H1. This higher than usual regularity requirement motivates the use of novel finite element spaces. Here we choose a C1 quadratic B-splines basis for the displacement field. A consistent, symmetric discretization in this space yields a discrete formulation that is underconstrained. Stabilizing with a least-squares penalty provides a stable, convergent discrete formulation. Computational examples validate this formulation and demonstrate numerical convergence with mesh refinement. Our results demonstrate that no explicit regularization of this inverse problem is needed. |