Motivation The Poisson problem has a strong formulation; a minimization formulation; and a weak formulation. The minimization/weak formulations are more general than the strong formulation in terms of reqularity and admissible data

1 Scalar Conservation laws 1.1 Definit 1.1.1 Conservative form

Integral Equation Methods Reminder about galerkin and Collocation Example of convergence issues in 1D First and second kind integral equations Develop some intuition about the difficulties Convergence for second kind equations Consistency and stability issues

Integral Equation Methods Reminder about Galerkin and collocation Example of convergence issues in 1D First and second kind integral equations Develop some intuition about the difficulties Convergence for second kind equations Consistency and stability issues Nystrom Method

Outline Easy technique for computing integrals Piecewise constant approach Gaussian Quadrature Convergence properties Essential role of orthogonal polynomials Multidimensional Integrals Techniques for singular kernels Adaptation and variable transformation Singular quadrature

1 Model problem 1.1 Formulations 1.1.1 Strong formulation LIDE Find a such that for Q a polygonal domain Generalizat ion We look here at a particularly simple but nevertheless illustrative problem

Goals Theory A priori A priori error estimates N1 bound various“ measures” of u exact]-un [approximate] in terms of C(n, problem parameters h [mesh diameter, and u

Outline Reminder about 1-D 1st and 2nd Kind egns Three-D Laplace Problems Interior Neumann Problem Null space issue First Kind Theory for 3-D Laplace Informal Convergence Theory

麻省理工学院：偏微分方程式数字方法（英文版）_lec26

2.1 机械手运动的表示方法 2.2 手爪位置和关节变量的关系 2.3 雅可比矩阵 2.4 手爪力和关节驱动力的关系 2.5 机械手运动方程式的求解