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Section: New Results

Cubature nodes for spectral element methods on symplicial meshes

Participants : Richard Pasquetti, Francesca Rapetti.

In a recent JCP paper (see [37]), a higher order triangular spectral element method ($T$SEM) is proposed to address seismic wave field modeling. The main interest of this $T$SEM is that the mass matrix is diagonal, so that an explicit time marching becomes very cheap. In [16], R. Pasquetti and F. Rapetti have compared this cubature points based method to the Fekete-Gauss one, that makes use of Fekete points for interpolation and of Gauss points for quadrature. Moreover, they have proposed an extension of this cubature $T$SEM to address elliptic PDEs with non homogeneous Neumann or Robin boundary conditions. More recently, the cubature $T$SEM has been experimented with isoparametric mappings to consider the case of non polygonal computational domains. In any cases it turns out that the cubature $T$SEM compares well with the Fekete-Gauss one.