ContentsBasic Theory of Standard Finite Element Method 11.1 The Basic Principles of Functional Analysis 11.1.1 Linear Operator and Linear Functional 11.1.2 Orthogonal Proj ection and Riesz Representation Theorem 41.1.3 Smooth Approximation and Fundamental Lemma of Calculus of Variation 51.1.4 Generalized Derivatives and Sobolev Spaces 61.1.5 Imbedding and Trace Theorems of Sobolev Spaces 91.1.6 Equivalent Module (Norm) Theorem 111.1.7 Green's Formulas, Riesz-Thorin��s Theorem,Interpolation Inequality, and Closed Range Theorem 181.1.8 Fixed Point Theorems 201.2 Well-Posedness of Partial Differential Equations 211.2.1 The Classification for the Partial Differential Equations 211.2.1.1 Physical Classification for Partial Differential Equations 211.2.1.2 Mathematical Classification for Partial Differential Equations 211.2.1.3 The Second-Order Eq (1.2.2) Does Not Change Its Fomi under the Invertible Transformation 221.2.1.4 The