Matlab Implementation of Stokes Equations
Budget: $10 – $30 USD
What I exactly need is having three methods (preconditioned Uzawa, preconditioned bramble-paciak and preconditioned Minres) applied on stokes equations. I need the numerical solutions/results, tables and graphs in order to compare the methods with each other and determine which method is the best. I need errors calculated using Soblev spaces and weak formulation of stokes equations.
I have done theoretically parts. I need numerical part. codes for the three methods that compute (u, p and errors). compute the time it takes for each method to reach a solution. graphs and tables
You must care that applying Preconditioned Uzawa, Preconditioned Minres and Preconditioned Bramble and Pasciak. You can use use FINITE ELEMENT package on matlab to solve Stokes equations
And don't forgot that in which discretization spaces you used
The plan is that you apply a finite element discretisation of Stokes (using an LBB stable pair), test whether it is correct, and once it is solve the matrix-vector system with the iterative methods you have studied.
It would be interesting to see how many iterations you need to reduce the norm of the initial residual with some large factor (say 10^-6).
I suggest for the moment only to test MINRES and Uzawa without preconditioners.
(The Bramble-Pasciak method can only applied when you have a preconditioner)
It is an important link to use it to build codes by using finite element discretization package:
https://lyc102.github.io/ifem/projects/Stokes/#part-i-isop2-p0-element
These are examples three thesis links to take a look at the numerical results to take an idea about numerical results and see tables and graphs:
https://cpb-us-w2.wpmucdn.com/sites.udel.edu/dist/1/11143/files/2022/01/gradUzawa12.pdf
https://typeset.io/pdf/inexact-and-preconditioned-uzawa-algorithms-for-saddle-point-42jmb0vx5u.pdf
https://arxiv.org/pdf/1309.5048.pdf
I have done theoretically parts. I need numerical part. codes for the three methods that compute (u, p and errors). compute the time it takes for each method to reach a solution. graphs and tables
You must care that applying Preconditioned Uzawa, Preconditioned Minres and Preconditioned Bramble and Pasciak. You can use use FINITE ELEMENT package on matlab to solve Stokes equations
And don't forgot that in which discretization spaces you used
The plan is that you apply a finite element discretisation of Stokes (using an LBB stable pair), test whether it is correct, and once it is solve the matrix-vector system with the iterative methods you have studied.
It would be interesting to see how many iterations you need to reduce the norm of the initial residual with some large factor (say 10^-6).
I suggest for the moment only to test MINRES and Uzawa without preconditioners.
(The Bramble-Pasciak method can only applied when you have a preconditioner)
It is an important link to use it to build codes by using finite element discretization package:
https://lyc102.github.io/ifem/projects/Stokes/#part-i-isop2-p0-element
These are examples three thesis links to take a look at the numerical results to take an idea about numerical results and see tables and graphs:
https://cpb-us-w2.wpmucdn.com/sites.udel.edu/dist/1/11143/files/2022/01/gradUzawa12.pdf
https://typeset.io/pdf/inexact-and-preconditioned-uzawa-algorithms-for-saddle-point-42jmb0vx5u.pdf
https://arxiv.org/pdf/1309.5048.pdf