A posteriori error estimates are arguably more useful than a priori esti mates since we know uh. Bear in mind, however, that (i) in most methods

1 Motivation The Poisson problem has a strong formulation a minimization formulation and a weak formulation T weak formulations are more general than the strong formulation in terms of regularity and admissible data SLIDE 2 The minimization/weak formulations are defined by: a space X; a bilinear The minimization/weak formulations identify ESSENTIAL boundary conditions NATURAL boundary conditions ed in a The points of departure for the finite element method are the weak formulation(more generally) the minimization statement (if a is SPD) 2 The dirichlet problem 2.1 Strong Formulation Find u such that

Poisson Equation in 1D Model Problem Boundary Value Problem(BVP) Wra(ac)= f(a) N1 x∈(0,1),w(0)=(1)=0,f∈C0N2 Describes many simple physical phen

1 Finite difference formulas 1.1 Problem definition We have seen that one of the necessary ingredients in devising finite differe

Governing Equation Stability Analysis 3 Examples Relationship between σ and λh Implicit Time-Marching Scheme

1 Background Brandt(1973)published first paper SLIDE 1 Offers the possibility of solving a problem with work and storage propor tional to the number of unknowns Well developed for elliptic proble

1 First Order ave Equation SLIDE 1 The simplest first order partial differential equation in two variables(a, t)is the linear wave equation. Recall that all first order PDE's are of hyperbolic type INITIAL BOUNDARY VALUE PROBLEM (IBVP) 0,x∈(0,1)

Despite its apparent simplicity this equation appears in a wide range of dis m heat 7 to financial er we will make extensive use of this equation, and several of the limiting cases contained therein, to illustrate the numerical techniques that will be presented

1 Model problem 1.1 Poisson Equation in 1D Boundary Value Problem(BVP) (x)=∫(x) (0,1),u(0)=(1)=0,f Describes many simple physical phenomena(e.g) Deformation of an elastic bar Deformation of a string under tension Temperature distribution in a bar The Poisson equation in one dimension is in fact an ordinary differ tion. When dealing with ordinary differential equations we Poisson equation will be used here to illastrate numerical techniques for elliptic PDE's in multi-dimensions. Other techniques specialized for ordinary differen tial equations could be used if we were only interested in the one dimension

一、机电传动系统的运动方程式； 二、多轴传动系统中转矩折算的基本原则和方法； 三、了解几种典型生产机械的负载特性； 四、了解机电传动系统稳定运行的条件以及学会分析实际系统的稳定性