Weak Formulation
Download
1 / 8

BVP - PowerPoint PPT Presentation


  • 200 Views
  • Uploaded on

Weak Formulation. BVP. Weak Formulation ( variational formulation). Multiply equation (1) by v(x) and then integrate from 0 to 1. Integration by parts yiels. where. Galerkin Methods. BVP. Unique sol?. Weak Formulation ( variational formulation). Infinite dimensional space. where.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about ' BVP' - clinton-cox


An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Weak Formulation

BVP

Weak Formulation ( variational formulation)

Multiply equation (1) by v(x) and then integrate from 0 to 1

Integration by parts yiels

where


Galerkin Methods

BVP

Unique sol?

Weak Formulation ( variational formulation)

Infinite dimensional space

where


Galerkin Methods

Weak Formulation ( variational formulation)

Infinite dimensional space

Unique sol?

Is finite dim


Galerkin Methods

Discrete Form

Is finite dim

We can approximate u


Galerkin Methods

Linear system

Unique sol?

  • Linear system of equation

  • square

  • Symmetric (why)

  • Positive definite


Finite Element Methods

Finite Element Methods

why

1

0

0.25

0.5

0.75

1

0

0.25

0.5

0.75


Finite Element Methods

Finite Element Methods

1

1

1

1

1

1

0

0

0

0.25

0.25

0.25

0.5

0.5

0.5

0.75

0.75

0.75


Finite Element Methods

HomeWork:

Compute the matrix A and the vector b then solve the linear system and write the solution as a linear combination of the basis then approximate the value of the function at x= 0.3, 0.7. can you find the analytic solution of the problem?

where h=1/4 f(x)= x(x-1) with pc-linear