The concept of a weak solution of a boundary value problem plays an important role in some numerical solutions including the finite element method. The idea of a "weak solution" can be a rather weak notion. The following problem was presented in lecture 3 of week 8. It is generally not solvable in closed form. 00 on 0
The concept of a weak solution of a boundary value problem plays an important role in some numerical solutions including the finite element method. The idea of a "weak solution" can be a rather weak notion. The following problem was presented in lecture 3 of week 8. It is generally not solvable in closed form. 00 on 0
Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
ChapterMA: Math Assessment
Section: Chapter Questions
Problem 1.1MA
Related questions
Question
![DISCUSSION
Before posting to the discussion board, complete the following:
The concept of a weak solution of a boundary value problem plays an important role in some numerical
solutions including the finite element method. The idea of a "weak solution" can be a rather weak notion.
The following problem was presented in lecture 3 of week 8. It is generally not solvable in closed form.
0<x<1, c(x) >0 on 0<x<1
-u"(x)+c(x)u(x)=f(x),
u(0)=0, u(1)=0
The weak form of this BVP was given as
where
a(u, v) = f(v), for all v EV
a(u, v) = f'(u'v' + cuv)dx, for all u,veV, (v)=f(x)v(x) dx, for all ve V
Post a response to the following discussion questions.
What value does the weak formulation offer?
What is the possible shortcoming of the weak formulation?
Does one arrive at a minimization problem by substituting v=du, the variation in u, ; i.e.. can one arrive at
an integral
such that yields the original equation?
1
V = [ f(u,u',x) dx
v
0](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc7559a47-bb34-494d-9e33-22c98791555e%2F64b4f3a4-b733-4af9-b68f-2d1aea5128a6%2Fey57ugf_processed.jpeg&w=3840&q=75)
Transcribed Image Text:DISCUSSION
Before posting to the discussion board, complete the following:
The concept of a weak solution of a boundary value problem plays an important role in some numerical
solutions including the finite element method. The idea of a "weak solution" can be a rather weak notion.
The following problem was presented in lecture 3 of week 8. It is generally not solvable in closed form.
0<x<1, c(x) >0 on 0<x<1
-u"(x)+c(x)u(x)=f(x),
u(0)=0, u(1)=0
The weak form of this BVP was given as
where
a(u, v) = f(v), for all v EV
a(u, v) = f'(u'v' + cuv)dx, for all u,veV, (v)=f(x)v(x) dx, for all ve V
Post a response to the following discussion questions.
What value does the weak formulation offer?
What is the possible shortcoming of the weak formulation?
Does one arrive at a minimization problem by substituting v=du, the variation in u, ; i.e.. can one arrive at
an integral
such that yields the original equation?
1
V = [ f(u,u',x) dx
v
0
Expert Solution
![](/static/compass_v2/shared-icons/check-mark.png)
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
![Blurred answer](/static/compass_v2/solution-images/blurred-answer.jpg)
Knowledge Booster
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.Recommended textbooks for you
![Elements Of Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
![Mechanics of Materials (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Thermodynamics: An Engineering Approach](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
![Elements Of Electromagnetics](https://www.bartleby.com/isbn_cover_images/9780190698614/9780190698614_smallCoverImage.gif)
Elements Of Electromagnetics
Mechanical Engineering
ISBN:
9780190698614
Author:
Sadiku, Matthew N. O.
Publisher:
Oxford University Press
![Mechanics of Materials (10th Edition)](https://www.bartleby.com/isbn_cover_images/9780134319650/9780134319650_smallCoverImage.gif)
Mechanics of Materials (10th Edition)
Mechanical Engineering
ISBN:
9780134319650
Author:
Russell C. Hibbeler
Publisher:
PEARSON
![Thermodynamics: An Engineering Approach](https://www.bartleby.com/isbn_cover_images/9781259822674/9781259822674_smallCoverImage.gif)
Thermodynamics: An Engineering Approach
Mechanical Engineering
ISBN:
9781259822674
Author:
Yunus A. Cengel Dr., Michael A. Boles
Publisher:
McGraw-Hill Education
![Control Systems Engineering](https://www.bartleby.com/isbn_cover_images/9781118170519/9781118170519_smallCoverImage.gif)
Control Systems Engineering
Mechanical Engineering
ISBN:
9781118170519
Author:
Norman S. Nise
Publisher:
WILEY
![Mechanics of Materials (MindTap Course List)](https://www.bartleby.com/isbn_cover_images/9781337093347/9781337093347_smallCoverImage.gif)
Mechanics of Materials (MindTap Course List)
Mechanical Engineering
ISBN:
9781337093347
Author:
Barry J. Goodno, James M. Gere
Publisher:
Cengage Learning
![Engineering Mechanics: Statics](https://www.bartleby.com/isbn_cover_images/9781118807330/9781118807330_smallCoverImage.gif)
Engineering Mechanics: Statics
Mechanical Engineering
ISBN:
9781118807330
Author:
James L. Meriam, L. G. Kraige, J. N. Bolton
Publisher:
WILEY