Chapter 1. Elliptic Boundary Value Problems and FEM 1.1 Elliptic Boundary Value Problems 1.2 Ritz-Galerkin Method 1.3 Finite Element Method (FEM) 1.4 Inverse Assumption 1.5 L oo Estimate 1.6 L p Estimate 1.

7 Asymptotic Expansion. Chapter 2. Semigroup Theory and FEM 2.1 Evolutionary Problems 2.2 Semi-discretization 2.3 Fractional Powers 2.4 Full-discretization 2.5 Inhomogeneous Equation 2.

6 Higher Accuracy 2.7 L oo Estimate 2.8 Hyperbolic Equation. Chapter 3. Evolution Equations and FEM 3.1 Generation Theories 3.2 A Priori Estimates 3.3 Semi-discretization 3.

4 Full-discretization 3.5 Alternative Approach. Chapter 4. Other Methods in Time Discretization 4.1 Rational Approximation of Semigroups 4.2 Multi-step Method 4.3 Product Formula. Chapter 5.

Other Methods in Space Discretization 5.1 Lumping of Mass 5.2 Upwind Finite Elements 5.3 Mixed Finite Elements 5.4 Boundary Element Methods (BEM) 5.5 Charge Simulation Methods (CSM). Chapter 6. Nonlinear Problems 6.

1 Semilinear Elliptic Equations 6.2 Semilinear Parabolic Equations 6.3 Degenerate Parabolic Equations. Chapter 7. Domain Decomposition Method 7.1 Dirichlet to Neumann (DN) Map 7.2 Dirichlet to Neumann (DN) Iteration 7.3 Dirichlet 2 to Neumann 2 (DD-NN) Iteration 7.

4 Robin to Robin Iteration 7.5 Exterior Problem 7.6 The Stokes System. Bibliography. Index.