Abstract
AbstractFor a class of fourth order gradient flow problems, integration of the scalar auxiliary variable (SAV) time discretization with the penalty‐free discontinuous Galerkin (DG) spatial discretization leads to SAV‐DG schemes. These schemes are linear and shown unconditionally energy stable. However, the reduced linear systems are rather expensive to solve due to the dense coefficient matrices. In this paper, we provide a procedure to pre‐evaluate the auxiliary variable in the piecewise polynomial space. As a result the computational complexity of reduces to when exploiting the conjugate gradient (CG) solver. This hybrid SAV‐DG method is more efficient and able to deliver satisfactory results of high accuracy. This was also compared with solving the full augmented system of the SAV‐DG schemes.
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