Resumen de On the computation of the stabilized coefficients for the 1D spectral VMS method

Soledad Fernández García , Tomás Chacón Rebollo

• In this work, we study the computation of the stabilized coefficients for the Variational Multi-Scale method with spectral approximation of the sub-scales, applied to 1D problems. The method is based on an extension of the spectral theorem to operators that have an associated base of eigenfunctions, which are orthonormal in weighted L2 spaces. We study the discretization of both second order elliptic and parabolic problems with the finite element method. The spectral VMS method is characterized as a standard VMS method with stabilized coefficients issued form the eigenfunctions of the sub-grid problem, that are computed analytically. We derive an off-line/on-line strategy for the computation of the stabilized coefficients. This allows a fast solution of the spectral VMS method, similar to that of the standard VMS one. We display some numerical tests for the stationary and evolutive one-dimensional advection–diffusion equations, in which observe super-convergence effects at the grid nodes.