Saray Busto Ulloa

Departamento de Matemática Aplicada, Universidade de Santiago de Compostela (USC), y CITMAga

Título: Towards structure-preserving methods for continuum mechanics

Resumen: Systems of partial differential equations arising in continuum mechanics are typically endowed with intrinsic physical and mathematical structures. These include thermodynamical compatibility in overdetermined systems, consistency with asymptotic limit models, the preservation of equilibrium states (C-property), and the enforcement of natural differential constraints. Ensuring that these structural features are faithfully conveyed to the discrete level is essential for obtaining physically meaningful and numerically robust solutions.

In this talk, we examine how various numerical approaches address these issues and discuss their relevance for the design of discretization methods. Through representative test cases and different discretization frameworks, we will analyse how they can be preserved and illustrate their impact on stability, accuracy, and physical fidelity of the computed solutions.