Arturo Hidalgo

TL;DR: The proposed scheme that combines for the first time high order ADER methods with space–time adaptive grids in two and three space dimensions is likely to become a useful tool in several fields of computational physics, applied mathematics and mechanics.

TL;DR: A novel arbitrary high order accurate discontinuous Galerkin (DG) finite element method on space–time adaptive Cartesian meshes (AMR) for hyperbolic conservation laws in multiple space dimensions, using a high order a posteriori sub-cell ADER-WENO finite volume limiter.

TL;DR: A new high order accurate centered path-conservative method on unstructured triangular and tetrahedral meshes for the solution of multi-dimensional non-conservative hyperbolic systems, as they typically arise in the context of compressible multi-phase flows.

TL;DR: A new efficient formulation of the local space-time discontinuous Galerkin predictor is derived using a nodal approach whose interpolation points are tensor-products of Gauss–Legendre quadrature points, with particular emphasis on the asymptotic preserving property for linear model systems and the compressible Navier–Stokes equations with chemical reactions.

TL;DR: The resulting basic flux is first-order accurate and monotone; it is extended to arbitrary order of accuracy in space and time on unstructured meshes in the framework of finite volume and discontinuous Galerkin methods.