We present an arbitrary order discontinuous Galerkin finite element method for solving the biharmonic interface problem on the unfitted mesh. The approximation space is constructed by a patch reconstruction process with at most one degree freedom per element. The discrete problem is based on the symmetric interior penalty method and the jump conditions are weakly imposed by the Nitsche's technique. The C^2-smooth interface is allowed to intersect elements in a very general fashion and the stability near the interface is naturally ensured by the patch reconstruction. We prove the optimal a priori error estimate under the energy norm and the L^2 norm. Numerical results are provided to verify the theoretical analysis.

翻译：我们提出了一种任意阶间断伽辽金有限元方法，用于在非拟合网格上求解双调和界面问题。近似空间通过单元修补重构过程构建，每个单元最多包含一个自由度。离散问题基于对称内部惩罚方法，并由Nitsche技术弱施加跳跃条件。允许\(C^2\)光滑界面以非常一般的方式与单元相交，且界面附近的稳定性通过修补重构自然得到保证。我们证明了能量范数和\(L^2\)范数下的最优先验误差估计，并提供了数值结果以验证理论分析。