A second-order maximum principle preserving continuous finite element technique for nonlinear scalar conservation equations

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Date(s) - 24/06/2014
11 h 00 min - 12 h 00 min


In the first part of the talk I will introduces a first-order
viscosity method for the explicit approximation of scalar conservation
equations with Lipschitz fluxes using continuous finite elements on
arbitrary grids in any space dimension. Provided the lumped mass matrix
is positive definite, the method is shown to satisfy the local maximum
principle under a usual CFL condition. The method is independent of the
cell type; for instance, the mesh can be a combination of tetrahedra,
hexahedra, and prisms in three space dimensions. An a priori convergence
estimate is given provided the initial data is BV.
In the second part of the talk I will extend the accuracy of the method
to second-order (at least). The technique is based on mass-lumping
correction, a high-order entropy viscosity method, and the
Boris-Book-Zalesak flux correction technique. The algorithm works for
arbitrary meshes in any space dimension and for all Lipschitz fluxes.
The formal second-order accuracy of the method and its convergence
properties are tested on a series of linear and nonlinear benchmark


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