Eduardo M. Garau

CONVERGENCE OF ADAPTIVE FINITE ELEMENT METHODS FOR EIGENVALUE PROBLEMS

In this article we prove convergence of adaptive finite element methods for second order elliptic eigenvalue problems. We consider Lagrange finite elements of any degree and prove convergence for simple as well as multiple eigenvalues under a minimal refinement of marked elements, for all reasonable marking strategies, and starting from any initial triangulation.

A posteriori error estimators for hierarchical B-spline discretizations

In this paper, we develop a function-based a posteriori error estimators for the solution of linear second-order elliptic problems considering hierarchical spline spaces for the Galerkin discretiza...

On Quasi-Interpolation Operators in Spline Spaces

We propose the construction of a class of L2 stable quasi-interpolation operators onto the space of splines on tensor-product meshes, in any space dimension. The estimate we propose is robust with respect to knot repetition and to knot “vicinity” (up to p + 1 knots), so it applies to the most general scenario in which the B-spline functions are known to be well defined.