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Isogeometric analysis for singularly perturbed high-order, two-point boundary value problems of reaction–diffusion type
Computers & Mathematics with Applications ( IF 2.9 ) Pub Date : 2020-05-28 , DOI: 10.1016/j.camwa.2020.05.011
C. Xenophontos

We consider two-point, reaction–diffusion type, singularly perturbed boundary value problems of order 2νZ+, and the approximation of their solution using isogeometric analysis. In particular, we use a Galerkin formulation with B-splines as basis functions, defined using appropriately chosen knot vectors. We prove robust exponential convergence in the energy norm, independently of the singular perturbation parameter. Numerical examples are also presented, which illustrate (and extend) the theory.



中文翻译:

反应扩散型奇摄动高阶两点边值问题的等几何分析

我们考虑两点反应扩散型奇异摄动阶边值问题 2νž+并用等几何分析逼近其解。特别地,我们使用的Galerkin制剂与B样条作为基函数,使用适当选择的节点向量定义。我们证明了能量范数中的鲁棒指数收敛性,与奇异摄动参数无关。还提供了数值示例,这些示例说明了(并扩展了)该理论。

更新日期:2020-05-28
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