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| f(x)i do dr. dr, dx dx where o's are the shape functions defined as piecewise linear polynomials. I. When f(x) = erp(r), the standard Gaussian numerical integration is able to integrate the above integral exactly. II. When f(x) = x5-1, the minimum number of Gauss points and corre- sponding weights to integrate above integral using standard Gaussian quadra- ture exactly is 3. III. When f(x) is polynomial of order n, with 3 Gauss points and weights, the maximum value of n can be 5 to integrate above exactly using standard Gaussian quadrature. %3D 4. Which of the above statements are true? O A) Only O B) Only i O C) Only li O D)l and B O EJLH and li

| f(x)i do dr. dr, dx dx where o's are the shape functions defined as piecewise linear polynomials. I. When f(x) = erp(r), the standard Gaussian numerical integration is able to integrate the above integral exactly. II. When f(x) = x5-1, the minimum number of Gauss points and corre- sponding weights to integrate above integral using standard Gaussian quadra- ture exactly is 3. III. When f(x) is polynomial of order n, with 3 Gauss points and weights, the maximum value of n can be 5 to integrate above exactly using standard Gaussian quadrature. %3D 4. Which of the above statements are true? O A) Only O B) Only i O C) Only li O D)l and B O EJLH and li

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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An example of an integral stemming from the finite element formulation, possible from a weak form of a boundary value problem for u containing a term f(x), is given by 7. dr2 dx dx where o's are the shape functions defined as piecewise linear polynomials. I. When f(x) = erp(x), the standard Gaussian numerical integration is able to integrate the above integral exactly. II. When f(r) = x - 1, the minimum number of Gauss points and corre- sponding weights to integrate above integral using standard Gaussian quadra- ture exactly is 3. III. When f(r) is polynomial of order n, with 3 Gauss points and weights, the maximum value of n can be 5 to integrate above exactly using standard Gaussian quadrature. Which of the above statements are true? O A) Only I B) Only II O C) Only il O D)l and iI O EJL Il and I
Transcribed Image Text:An example of an integral stemming from the finite element formulation, possible from a weak form of a boundary value problem for u containing a term f(x), is given by 7. dr2 dx dx where o's are the shape functions defined as piecewise linear polynomials. I. When f(x) = erp(x), the standard Gaussian numerical integration is able to integrate the above integral exactly. II. When f(r) = x - 1, the minimum number of Gauss points and corre- sponding weights to integrate above integral using standard Gaussian quadra- ture exactly is 3. III. When f(r) is polynomial of order n, with 3 Gauss points and weights, the maximum value of n can be 5 to integrate above exactly using standard Gaussian quadrature. Which of the above statements are true? O A) Only I B) Only II O C) Only il O D)l and iI O EJL Il and I
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