《有限元方法的数学理论》中不但提供有限元法系统的数学理论。还兼重在工程设计和分析中的应用算法效率、程序开发和较难的收敛问题。目次：基本概念；Sobolev空间；椭圆边界值问题变分公式；有限元空间结构；Sobolev空间中的多项式近似理论．n维变分问题；有限元多栅法；加性Schwarz预条件； 极大范数估计；自适应网格； 变分病态、在平面弹性力学中的应用；混合法；迭代技巧用于混合法；算子插值理论的应用。读者对象；数学、物理和工程专业的研究生和技术人员。-" The mathematical theory of finite element method"　in the finite element method system not only provides the mathematical theory. And also focuses on engineering design and analysis of efficiency of the algorithm, program development and the convergence problem more difficult. Table of Contents: Basic concepts　Sobolev space　elliptic boundary value problems variational formulation　finite element spatial structure　Sobolev space theory of polynomial approximation. n-dimensional variational problem　finite element multi-grid method　additive Schwarz preconditioner　maximum norm estimate　adaptive grid　pathological variation in the plane elasticity in the application　mixed　iterative techniques for mixed method　Operator Interpolation Theory. Readers　mathematics, physics and engineering graduate students and technical staff.