论文标题
傅立叶系列（基于）科学与工程中计算分析的多尺度方法：ii。复合傅立叶系列方法，用于同时近似函数及其（部分）衍生物
Fourier series (based) multiscale method for computational analysis in science and engineering: II. Composite Fourier series method for simultaneous approximation to functions and their (partial) derivatives
论文作者
论文摘要
傅立叶系列多尺度方法是一种简洁有效的多尺度计算方法，将根据这一系列论文开发。第二篇论文与函数及其（部分）衍生物的同时近似有关。根据足够的条件，2R（R是一个积极的整数）时间逐期限的傅里叶序列差异，一个二维或二维功能与一般边界条件分解为角函数的线性组合，该函数描述了域名的不连续性（仅在二维功能上描述了二维功能），该功能是在二维功能上描述了跨性别的功能，该功能是跨性别的函数，该函数是跨性别函数的域名，该功能是跨性别函数的界限，而构造了域的界限。域内的平稳性。它导致具有复合傅立叶序列的功能及其（部分）衍生物的同时近似方法。具体而言，对于基于代数多项式的综合傅立叶序列方法，理论上分析了完整代数多项式的复制特性，并使用数值示例验证了近似精度。这项研究将傅立叶系列方法概括为具有补充术语的功能及其（部分）衍生物的同时近似，最高为2r阶。
Fourier series multiscale method, a concise and efficient analytical approach for multiscale computation, will be developed out of this series of papers. The second paper is concerned with simultaneous approximation to functions and their (partial) derivatives. On the basis of sufficient conditions of 2r (r is a positive integer) times term-by-term differentiation of Fourier series, a one-dimensional or two-dimensional function with general boundary conditions is decomposed into the linear combination of a corner function that describes the discontinuities at corners of the domain (only for the two-dimensional function), boundary functions that describe the discontinuities on boundaries of the domain and an internal function that describes the smoothness within the domain. It leads to the methodology of simultaneous approximation of functions and their (partial) derivatives with composite Fourier series. And specifically, for the algebraical polynomial based composite Fourier series method, the reproducing property of complete algebraical polynomials is theoretically analyzed and the approximation accuracy is validated with numerical examples. This study generalizes the Fourier series method with supplementary terms to simultaneous approximation of functions and their (partial) derivatives up to 2rth order.
