具有奇异热源的广义布森斯克方程的精确无发散混合非连续伽勒金方法

Haitao Leng
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引用次数: 0

摘要

本研究的目的是针对具有奇异热源的广义布森斯克方程提出并分析一种混合非连续伽勒金(HDG)方法。我们使用 k、k-1 和 k 阶多项式来逼近速度、压力和温度。通过为压力引入拉格朗日乘法器,HDG 方法得到的近似速度场被证明是完全无发散和符合 H(div)的。在问题数据和解的小性假设下,我们通过布劳威尔定点定理证明了离散系统在两个维度上有一个解。如果进一步假设粘度和热导率为正常数,则可得出收敛率为 O(h)的先验误差估计和高效可靠的后验误差估计。最后用数值示例说明了理论分析,并展示了所获得的后验误差估计的性能。1991 年数学学科分类65N12,65N30,65N50,76N05。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
An exactly divergence-free hybridized discontinuous Galerkin method for the generalized Boussinesq equations with singular heat source
The purpose of this work is to propose and analyze a hybridized discontinuous Galerkin (HDG) method for the generalized Boussinesq equations with singular heat source. We use polynomials of order k, k−1 and k to approximate the velocity, the pressure and the temperature. By introducing Lagrange multipliers for the pressure, the approximate velocity field obtained by the HDG method is shown to be exactly divergence-free and H(div)-conforming. Under a smallness assumption on the problem data and solutions, we prove by Brouwer’s fixed point theorem that the discrete system has a solution in two dimensions. If the viscosity and thermal conductivity are further assumed to be positive constants, a priori error estimates with convergence rate O(h) and efficient and reliable a posteriori error estimates are derived. Finally numerical examples illustrate the theoretical analysis and show the performance of the obtained a posteriori error estimator. 1991 Mathematics Subject Classification 65N12, 65N30, 65N50, 76N05.
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