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Explore a technical seminar presentation where Svetlana Tokareva from Los Alamos National Laboratory discusses advanced finite element methods for hyperbolic problems. Delve into the development of a mass-matrix-free finite element scheme that delivers explicit and arbitrary high-order approximations for hyperbolic PDEs in both space and time domains. Learn how the innovative design enables efficient mass matrix diagonalization without compromising accuracy through the integration of FEM formulation with Deferred Correction methodology. Understand the advantages of this matrix-free approach, including its compact approximation stencil at high orders, reduced computational costs compared to traditional finite element techniques, and potential benefits for exascale computing. Examine the staggered grid MF-FEM scheme for Lagrangian hydrodynamics through challenging benchmark problem simulations, and discover how structure-preserving properties like positivity and local bounds preservation are maintained using convex limiting techniques.
