A Priori Error Estimate for H1$$ {H}^1 $$ Galerkin Mixed Virtual Element Discretization of Parabolic Equations

ABSTRACT In this article, Galerkin‐mixed virtual element dicretization of parabolic equations is investigated by splitting the governing equation into a first‐order mixed system. The unknown function and flux function are approximated by different virtual element space resepctively. Compared with the standard mixed virtual element methods the new scheme relaxes the restrict of virtual element spaces. A priori error estimates for semidiscrete and fully discrete Galerkin mixed virtual element scheme are derived. Numerical examples are presented to demonstrate the theoretical results.