Local tangential lifting virtual element method for the diffusion-reaction equation on the non-flat Voronoi discretized surface

In this paper, we propose the surface virtual element method (SVEM) combining with the local tangential lifting technique (LTL) to solve the diffusion-reaction (DR) equation on the non-flat Voronoi discretized surface embedded in R-3. It has been a challenge on how to design the efficient numerical method to treat the non-flat discretized surface in comparison with the easy construction of flat discretized surface. Limited to the linear virtual element space, we derive the computable virtual element form of the non-flat Voronoi discretized surface by lifting the Voronoi element into the tangential plane. We demonstrate that this method developed here presents a good numerical simulation on a wide variety of polygonal discretized surfaces. Finally, numerical experiments are carried out to show the efficiency of the proposed method.