Description:
<jats:title>Abstract</jats:title>
<jats:p>In this paper, we use the mixed direct discontinuous Galerkin method (DDG) to solve the biharmonic equation. Firstly, by introducing an auxiliary variable, the biharmonic equation is split into two second-order equations. Secondly, the variational problem based on the DDG method of the system is derived and its well-posedness is proven. Next, error estimates of the approximate solution in <jats:italic>L</jats:italic>
<jats:sup>2</jats:sup> norm and energy norm are present. For a given polynomial degree <jats:italic>k</jats:italic> (<jats:italic>k</jats:italic> ≥ 1), the optimal convergence rates concerning energy norm and norm are <jats:italic>k</jats:italic> and <jats:italic>k</jats:italic> + 1, respectively. Finally, numerical results demonstrate the accuracy and capability of the method.</jats:p>