Abstract
In this paper, we propose an augmented subspace method for solving semilinear parabolic equations based on the Symmetric Interior Penalty Discontinuous Galerkin (SIPDG) method. The main idea of this method is, at each time step, to convert the solution of the semilinear elliptic problem into the solution of the corresponding linear boundary value problem on the same-scale discontinuous finite element space and the solution of the semilinear elliptic problem on a newly defined low-dimensional augmented subspace. The prior error estimates are derived. Numerical experiments are conducted to confirm the theoretical conclusions and the computing efficiency of the proposed method.
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