Questions tagged [convergence]

Questions related to whether the sequence of iterates generated by an iterative method has one or more limit points, and if those limit points have the correct properties.

57 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
0
votes
0answers
63 views

A name for a numerical phenomena when using numerical methods

I have a nonlinear solver for equation $g= c_1f(x_1,y_1)+c_2f(x_2,y_2)$. Note that $c_1$ is much bigger than $c_2$. So after using Levenberg–Marquardt algorithm, I could only get $x_1$, $y_1$ and $...
0
votes
0answers
93 views

Why does GMRES converge much slower for large Dirichlet boundary conditions?

I'm trying to numerically solve a simple Laplace equation in 2D, with a nonlinear source term: $\nabla^2 u = u^2$ with boundary conditions as $u=0$ everywhere except for $y=1$ where $u=u_0$. I'm ...
0
votes
0answers
33 views

Fit exponential convergence

I'm working with a numerical algorithm whose output $y$ asymptotically approaches a certain unknown value $a$. I expect an exponential convergence, i.e. the data $y$ given by my algorithm should be ...
0
votes
0answers
54 views

Correct order of convergence

I have a sequence of points which was obtained from an iterative algorithm, and I computed the order of convergence $p$ of the method using the formula $$ p \approx \frac{\log({\rm err}(k+2))-\log({\...
0
votes
0answers
184 views

Iterative algorithm prove precise conditions for convergence

Question: Consider the iterative improvement algorithm below. Starting with $Az_i = r_i$ and $(A + E)\hat{z}_i = r_i$ derive a formula showing how the absolute error in the $(i + 1)^{st}$ iterate $\...
0
votes
0answers
3k views

Stationary solution converge but time dependent doesn't

I've coupled a COMSOL model for fluid dynamics with a very simple pde that model the transport of humidity in air. When I solve it for the stationary case, the solution converge easily, but when I ...
-1
votes
1answer
127 views

Finite element convergence rate and possion's ratio

I am running simulations of a cantilever beam where it is fixed on one end and negative force applied to the other end. The first simulation is with 4-node linear quadrilateral elements and the other ...

1
2