Abstract The multiblock mortar expanded mixed method is explored to solve the second order linear elliptic problem. In this method, the domain is expressed as a union of smaller blocks (subdomains) separated by interface. The original problem is posed on each block and discretized locally. A scalar unknown is introduced on the shared boundaries between the blocks which is treated as Dirichlet boundary condition for the local problem. A special finite element space is constructed on the interface which serve as Lagrange multiplier to impose flux continuity across the inter-block boundaries. The mortar space is also used to approximate the scalar variable introduced on interface. We applied expanded mixed method to solve the local problem on each block and derived the error estimates for scalar, its gradient and its flux. We established the optimal order convergence rates for subdomain approximations. An error bound for mortar pressure is also presented. The computation is performed by transforming the algebraic system encounter by formulation into the positive definite problem in mortar space. An algorithm illustrating the implementation of method is also provided. The numerical experiments confirming theoretical results are also provided.

中文翻译：

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椭圆问题多块砂浆扩展混合法的先验误差估计

摘要 探索多块砂浆膨胀混合法求解二阶线性椭圆问题。在这种方法中，域表示为由接口分隔的较小块（子域）的联合。最初的问题是在每个块上提出并在本地离散化。在块之间的共享边界上引入了一个标量未知数，它被视为局部问题的狄利克雷边界条件。在界面上构建了一个特殊的有限元空间，用作拉格朗日乘子以在块间边界上施加通量连续性。迫击炮空间也用于逼近界面上引入的标量变量。我们应用扩展混合方法来解决每个块上的局部问题，并推导出标量、梯度和通量的误差估计。我们为子域逼近建立了最优阶收敛率。还提供了砂浆压力的误差界限。计算是通过将公式中遇到的代数系统转换为迫击炮空间中的正定问题来执行的。还提供了说明方法实现的算法。还提供了证实理论结果的数值实验。