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BCAMSevero Ochoa Award

basque center for applied mathematics

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Donat, Rosa

External Scientific Member

Linear and Non-Linear Waves

Alameda Mazarredo 14. 48009 Bilbao Basque Country - Spain


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.

Eusko Jaurlaritza - Gobierno Vasco ikerbasque - Basque Foundation for Science Bizkaia xede. Bizkaiko Foru Aldundia innobasque - Agencia vasca de la innovación Universidad del País Vasco (UPV/EHU) Ayuntamiento de Bilbao - Bilboko Udala