具有 Tresca 边界条件的斯托克斯流的非连续 Galerkin 方案：迭代后验误差分析

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Advances in Computational Mathematics Pub Date : 2024-11-25 DOI:10.1007/s10444-024-10207-7

J.K. Djoko, T. Sayah

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引用次数: 0

摘要

在两个维度上，我们提出并分析了摩擦型边界条件下斯托克斯方程的非连续 Galerkin 有限元近似的迭代后验误差指标。这里确定了两个误差来源，即离散化误差和线性化误差。在数据较小的假设条件下，我们证明了所设计的误差估算器是可靠的。平衡这两个误差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示例来说明这一理论。

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Discontinuous Galerkin schemes for Stokes flow with Tresca boundary condition: iterative a posteriori error analysis

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.

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来源期刊

Advances in Computational Mathematics 数学-应用数学

CiteScore

3.00

自引率

5.90%

发文量

审稿时长

3 months

期刊介绍： Advances in Computational Mathematics publishes high quality, accessible and original articles at the forefront of computational and applied mathematics, with a clear potential for impact across the sciences. The journal emphasizes three core areas: approximation theory and computational geometry; numerical analysis, modelling and simulation; imaging, signal processing and data analysis. This journal welcomes papers that are accessible to a broad audience in the mathematical sciences and that show either an advance in computational methodology or a novel scientific application area, or both. Methods papers should rely on rigorous analysis and/or convincing numerical studies.