In this work, semi-discrete and fully-discrete error estimates are derived for the Biot's consolidation model described using a three-field finite element formulation. The fields include displacements, total stress and pressure. The model is implemented using a backward Euler discretization in time for the fully-discrete scheme and validated for benchmark examples. Computational experiments presented verifies the convergence orders for the lowest order finite elements with discontinuous and continuous finite element appropriation for the total stress.

中文翻译：

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Biot固结模型总应力变量的有限元方法

在这项工作中，使用三场有限元公式描述的 Biot 固结模型推导出半离散和完全离散误差估计。这些场包括位移、总应力和压力。该模型是针对完全离散方案及时使用后向欧拉离散化实现的，并针对基准示例进行了验证。提供的计算实验验证了最低阶有限元的收敛阶数，其中总应力的不连续和连续有限元适用。