Variational multiscale virtual element method for the convection-dominated diffusion problem
The authors propose and analyze a stabilized multiscale virtual element method for the numerical solution of convection-diffusion equations on two-dimensional polygonal domains, which are equipped with homogeneous Dirichlet boundary conditions. The focus is on the equations with the dominated convection term, which makes the numerical solution a challenging problem because without any stabilization spurious oscillations can occur. The proposed method combines a variational multiscale method and a virtual element method with linear elements. The stabilization term is symmetric, positive, and does not depend on any parameter that has to be chosen by the user. Furthermore, compared to other stabilization techniques for these types of equations, the advantage is also the simple computation of the stabilization term. The authors analyze the stability of the proposed method and derive error estimates with respect to the \(L^2\) and \(H^1\) norms. Numerical experiments are presented to confirm the theoretical results and illustrate the efficiency of the proposed method.
scientific article; zbMATH DE number 7340763
scientific article