Analysis of an SUPG-stabilized virtual element method for scalar hyperbolic equations

In this work, we propose an SUPG Virtual Element discretization for scalar hyperbolic equations on general polygonal meshes. The analysis includes the coercivity of the discrete form with respect to a suitable convective norm, the well-posedness of the discrete problem, and the a priori error estimates consistent with classical finite element theory. We establish an almost uniform error bound, in which the dependence on unfavorable problem parameters is offset by higher-order mesh-size terms. Numerical experiments validate the accuracy and robustness of the method.