Donat, Rosa
A large part of my research activity has been devoted to the analysis and
design of numerical schemes for hyperbolic problems and, in particular, to
those questions related to the fact that non-oscillatory nonlinear
reconstruction techniques need to be considered in order to design state of
the art numerical schemes for shock computations. In collaboration with A.
Harten, I started exploring in the early nineties a new framework for
multi-resolution analysis of data and its application to the design of
cost-effective multilevel numerical
schemes for hyperbolic conservation laws and systems. In Harten's
multi-resolution framework nonlinearity can be easily introduced in a
conceptually straightforward manner by incorporating nonlinear
reconstruction techniques at the basic design level. Stability is the main
issue here, which I contributed to clarify in collaboration with F.
Arándiga. This activity has also led to different applications in
signal and image compression. In recent times, my interests include also
the analysis and applications of nonlinear approximation techniques in
subdivision schemes with specific properties, such as monotonicity or
convexity preservation in the recursive generation of data.
