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Convergence analysis of virtual element methods for semilinear parabolic problems on polygonal meshes

In this article, we discuss and analyze new conforming virtual element methods (VEMs) for the approximation of semilinear parabolic problems on convex polygonal meshes in two spatial dimension. The spatial discretization is based on polynomial and suitable nonpolynomial functions, and a Euler backward scheme is employed for time discretization. The discrete formulation of both the proposed schemes—semidiscrete and fully discrete (with time discretization) is discussed in detail, and the unique solvability of the resulted schemes is discussed. A priori error estimates for the proposed schemes (semidiscrete and fully discrete) in H1‐ and L2‐norms are derived under the assumption that the source term f is Lipschitz continuous. Some numerical experiments are conducted to illustrate the performance of the proposed scheme and to confirm the theoretical convergence rates.