Abstract Within the last years pressure robust methods for discretization of incompressible fluids have been developed. These allow use standard finite elements solution problem while simultaneously removing a spurious influence in approximation error velocity fluid, or displacement an solid. To this end, reconstruction operators are utilized mapping discretely divergence free functions to func...

Elasticity imaging can be understood as the intersection of the study of biomechanical properties, imaging sciences, and physics. It was mainly motivated by the fact that pathological tissue presents an increased stiffness when compared to surrounding normal tissue. In the last two decades, research on elasticity imaging has been an international and interdisciplinary pursuit aiming to map the ...

Conventional diagnostic ultrasound images portray differences in the acoustic properties of soft tissues, whereas ultrasound-based elasticity images portray differences in the elastic properties of soft tissues (i.e. stiffness, viscosity). The benefit of elasticity imaging lies in the fact that many soft tissues can share similar ultrasonic echogenicities, but may have different mechanical prop...

The particle–partition of unity method (PUM) [1, 2, 3, 4, 5, 8] is a meshfree Galerkin method for the numerical treatment of partial differential equations (PDE). In essence, it is a generalized finite element method (GFEM) which employs piecewise rational shape functions rather than piecewise polynomial functions. The PUM shape functions, however, make up a basis of the discrete function space...

Dual-Primal FETI methods are nonoverlapping domain decomposition methods where some of the continuity constraints across subdomain boundaries are required to hold throughout the iterations, as in primal iterative substructuring methods, while most of the constraints are enforced by Lagrange multipliers, as in one-level FETI methods. The purpose of this article is to develop strategies for selec...