A New Triangular Spectral Element Method Ⅱ:Mixed Formulation and $hp$-Error Estimates
A New Triangular Spectral Element Method Ⅱ:Mixed Formulation and $hp$-Error Estimates
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一种新的三角谱元方法Ⅸ：混合公式和$hp$-误差估计
DOI：
10.4208/nmtma.oa-2018-0038
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发表时间：
2019
期刊：
影响因子：
--
通讯作者：
Xie Ziqing
中科院分区：
文献类型：
--
作者：
Zhou Bingzhen;Wang Bo;Wang Lilian;Xie Ziqing
本文研究了非结构网格上基于节点基的混合三角谱元方法。该方法基于椭圆问题的等价一阶系统和矩形-三角形变换。该方法充分利用了节点基和非结构三角形网格处理复杂区域的张量结构和灵活性。与通常的Galerkin格式不同，混合形式在这种情况下特别有利，因为它可以避免矩形-三角形变换在矩阵计算中引起的奇异性，给出了该方法的先验误差估计，给出了实现细节和数值算例，验证了该方法的准确性和灵活性。
Mixed triangular spectral element method using nodal basis on unstructured meshes is investigated in this paper.The method is based on equivalent first order system of the elliptic problem and rectangle-triangle transforms.It fully enjoys the tensorial structure and flexibility in handling complex domains by using nodal basis and unstructured triangular mesh.Different from the usual Galerkin formulation,the mixed form is particularly advantageous in this context,since it can avoid the singularity induced by the rectangle-triangle transform in the calculation of the matrices,and does not require the evaluation of the stiffness matrix.An $hp$ a priori error estimate is presented for the proposed method.The implementation details and some numerical examples are provided to validate the accuracy and flexibility of the method.