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半线性分数阶扩散方程的时空有限元方法：间断Galerkin方法
  • ISSN号：1001-9847
  • 期刊名称：《应用数学》
  • 时间：0
  • 分类：O242.21[理学—计算数学;理学—数学]
  • 作者机构：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021
  • 相关基金：Foundation item： Supported by the National Natural Science Fund （11061021）, the National Science Foundation of Inner Mongolia（2012MS0106） ,and the Endancing Comprehensive Strength Projeet of Inner Mongolia University（14020202）
作者： 刘金存[1], 李宏[1]
关键词： 分数阶扩散方程, 间断GALERKIN方法, 存在唯一性, 误差估计, Fractional diffusion equation, Discontinuous Galerkin method , Existence and uniqueness, Error estimate
中文摘要：

本文研究半线性分数阶扩散问题的Galerkin时空有限元方法，该方法在空间连续，而在时间上间断．将有限元与有限差分方法相结合，充分利用拉格朗日插值多项式在Radau点处的特性，给出弱解的存在唯一性证明，且不需对时空网格施加任何限制．通过引入椭圆投影算子，详细导出了最优阶L∞（L^2）模误差估计．

英文摘要：

A Galerkin space-time finite element method, continuous in space but discontinuous in time, for the semilinear fractional diffusion problem is discussed. Based on a combination of finite element and finite difference techniques,taking full advantage of useful properties of Lagrange interpolation polynomials at the Radau points of each I,, the existence and uniqueness of the weak solution are proved without any assumption on the choice of space-time meshes. After introduce an appropriate elliptic projection operator,the optimal order error estimate in L^∞ （L^2） is derived in detail.

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期刊信息
  • 《应用数学》
  • 北大核心期刊（2011版）
  • 主管单位:国家教育部
  • 主办单位:华中科技大学
  • 主编：李大潜
  • 地址：武汉珞喻路1037号华中科技大学逸夫科技大楼南楼902室
  • 邮编：430074
  • 邮箱：yysx_hust@163.com
  • 电话：027-87543831
  • 国际标准刊号：ISSN：1001-9847
  • 国内统一刊号：ISSN：42-1184/O1
  • 邮发代号:38-61
  • 获奖情况:
  • 中国科学引文数据库来源期刊,中国学术期刊综合评价数据库来源期刊
  • 国内外数据库收录:
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  • 被引量:4139