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Weak Galerkin finite element methods combined with Crank-Nicolson scheme for parabolic interface problems
Bhupen Deka,Papri Roy,Naresh Kumar
Keywords:Parabolic, interface, finite element method, weak Galerkin method, optimal error estimates, low regularity, Crank-Nicolson
      This article is devoted to the a priori error estimates of the fully discrete Crank-Nicolson approximation for the linear parabolic interface problem via weak Galerkin finite element methods (WG-FEM). All the finite element functions are discontinuous for which the usual gradient operator is implemented as distributions in properly defined spaces. Optimal order error estimates in both $H^1$ and $L^2$ norms are established for lowest order WG finite element space $({\cal P}_{k}(K),\;{\cal P}_{k-1}(\partial K),\;\big[{\cal P}_{k-1}(K)\big]^2)$. Finally, we give a numerical example to verify the theoretical results.