非线性Sobolev-Galpern型方程的超收敛分析

Superconvergence analysis of nonlinear Sobolev-Galpern equations

摘要

用低阶混合有限元(Q ₁₁+Q ₀₁×Q ₁₀)研究非线性Sobolev-Galpern型方程。利用双线性元Q ₁₁及Q ₀₁×Q ₁₀元的高精度结果和平均值技巧,得到方程半离散格式的O(h ²)阶超收敛结果。对于方程线性化的全离散格式,得到具有O(h ²+τ ²)阶的超收敛结果,其中h是空间剖分参数,τ是时间步长。最后,通过数值算例证实理论分析的正确性。

Abstract

The nonlinear Sobolev-Galpern equations are studied with low order mixed finite element (Q ₁₁+Q ₀₁×Q ₁₀). By utilizing the high precision results of the finite element Q ₁₁+Q ₀₁×Q ₁₀, and mean-value technique, the superconvergence results of order O(h ²) are obtained for the semi-discrete scheme of the equations. For the linearized fully discrete scheme, the superconvergence results of order O(h ²+τ ²) are also derived, here h is the subdivision parameter, τ is the time step. Finally, a numerical example is provided to confirm our theoretical analysis.

关键词

非线性Sobolev-Galpern型方程 / 混合有限元 / 线性化格式 / 超收敛分析

Key words

nonlinear Sobolev-Galpern equations / mixed finite element / linearized scheme / superconvergence analysis

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基金资助

国家自然科学基金资助项目(11671369)