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Volume 10, Number 4, 2020, Pages 1433-1442                                                                DOI:10.11948/20190218
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.
Abstract:
      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 $L^{\infty}(H^1)$ and $L^{\infty}(L^2)$ 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 numerical examples to verify the theoretical results.
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