The course consists of two parts, namely finite difference methods for elliptic, parabolic and hyperbolic partial differential equations; the consistency, truncation error, stability and convergence analysis; some most commonly used methods for stability analysis for finite element methods, such as the Fourier analisis, the maximum Principle, energy method, etc.; the modified equation analysis of finite element methods, dissipation and dispersion of finite difference schemes; the general frame work of finite element method; a priori and a postriori error estimation as well as adaptive methods for second order elliptic equations, etc.
Mathematics
数学源自于古希腊语，是研究数量、结构、变化以及空间模型等概念的一门学科。透过抽象化和逻辑推理的使用，由计数、计算、量度和对物体形状及运动的观察中产生。数学的基本要素是：逻辑和直观、分析和推理、共性和个性。
