PRINCIPLES OF NUMERICAL CALCULATIONS
1 The Standard Galerkin Method 1 2 Methods Based on More General Approximations of the Elliptic Problem 25 3 Nonsmooth Data Error Estimates 37 4 More General Parabolic Equations 55 5 Negative Norm Estimates and Superconvergence 67 6 Maximum-Norm Estimates and Analytic Semigroups 81 7 Single Step Fully Discrete Schemes for the Homogeneous Equation 111 8 Single Step Fully Discrete Schemes for the Inhomogeneous Equation 129 9 Single Step Methods and Rational Approximations of Semigroups 149 10 Multistep Backward Difference Methods 163 11 Incomplete Iterative Solution of the Algebraic Systems at the Time Levels 185 12 The Discontinuous Galerkin Time Stepping Method 203 13 A Nonlinear Problem 231 14 Semilinear Parabolic Equations 245 15 The Method of Lumped Masses 261 16 The H1 and H?1 Methods 279 17 A Mixed Method 293 18 A Singular Problem 305 19 Problems in Polygonal Domains 317 20 Time Discretization by Laplace Transformation and Quadrature 335 References 355