Abstract
A conforming virtual element method is studied for approximating the solution of a pulsed electric interface model on polygonal meshes with small edges or faces, which traditional virtual and finite element methods cannot easily handle. One of the significant advantages of this virtual element method is to generate interface-conforming meshes efficiently exploiting polygonal meshes and hanging nodes. The virtual element method employs specific projection operators to establish optimal error estimates with reasonable assumptions regarding the solution's regularity. The voltage potential of the pulsed electric model through the physical media is approximated by using a fully discrete virtual element approach based on Crank-Nicolson temporal discretization. Numerical examples are used to illustrate the expected order of convergence. The efficiency and robustness of the proposed method are displayed on interface-independent/dependent background-fitted meshes with small edges and large magnitudes of discontinuities across the interface by these experiments.
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