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Discontinuous Galerkin schemes for Stokes flow with Tresca boundary condition: iterative a posteriori error analysis
Advances in Computational Mathematics ( IF 1.7 ) Pub Date : 2024-11-25 , DOI: 10.1007/s10444-024-10207-7
J.K. Djoko, T. Sayah

In two dimensions, we propose and analyse an iterative a posteriori error indicator for the discontinuous Galerkin finite element approximations of the Stokes equations under boundary conditions of friction type. Two sources of error are identified here, namely; the discretisation error and the linearization error. Under a smallness assumption on data, we prove that the devised error estimator is reliable. Balancing these two errors is crucial to design an adaptive strategy for mesh refinement. We illustrate the theory with some representative numerical examples.



中文翻译:


具有 Tresca 边界条件的 Stokes 流的不连续 Galerkin 方案:迭代后验误差分析



在二维中,我们提出并分析了在摩擦类型边界条件下斯托克斯方程的间断伽辽金有限元近似的迭代后误差指标。这里确定了两个错误来源,即;离散化误差和线性化误差。在数据的小假设下,我们证明了设计的误差估计器是可靠的。平衡这两个错误对于设计网格细化的自适应策略至关重要。我们用一些有代表性的数值例子来说明这个理论。

更新日期:2024-11-25
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