# 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.

153 questions
Filter by
Sorted by
Tagged with
50 views

### Why GA convergence curves continue as two parallel lines?

I'm working on a optimization problem and using GA algorithm (in MATLAB, ga function). As you know MATLAB plots GA result with two curves, one for the best values and other to show the mean values ...
179 views

### Implications of thermodynamic inconsistency in CFD calculations

During my PhD work, I had to use tabulated values of thermodynamic properties of gases in some Computational Fluid Dynamics (CFD in short) simulations. My tables are discretized in temperature and ...
107 views

### How the gmres method iteration behaves for this **enfant terrible** matrix?

Recently, I have been studied my lessons about gmres iteration, probably the most popular iteration method for general large sparse linear system of equations Ax=b. And the convergence is obtained ...
32 views

### Divergence issues when using intrinsic cohesive elements approach

When I model the strain localisation of a microscopic sample (or say RVE ) with cohesive elements approach, the convergence performance looks very terrible. I have to use extremely time increments (...
48 views

### Conjugate Gradient for singular 2D poisson finite element with Neumann Boundary Conditions

Heavily edited question after I realised partly what the problem was I have programmed a simple 2D square finite element solution to the Poisson equation $-\Delta u = f$ The source function ...
83 views

### Number of GMRES iterations increase when stepping forward in time, using the Newton method

I am solving a system of nonlinear time-dependent equations using the Newton method in a finite-element-setting, i.e. first I create the jacobian matrix for the current time, and afterwards I try to ...
23 views

560 views

306 views

### Line search bracketing for proximal gradient. Is it good idea?

Maybe my question is obvious but i cannot find any good source which answers it I trying to learn about proximal gradient. One thing which is not clear for me is particular algorithm for line search. ...
94 views

### Relationship between global and local error?

In some cases I have seen that if the local error is: $Err = O (\Delta t^{p+1})$ where the global error is p. So if local error is 3, global will be 2. Does somebody know where it comes? For ...
119 views

### In numerical methods, eg, finite differencing approaches, does there exist convergent schemes that are not both consistent and stable?

In a book that our course is following this semester, the theorem given is only in one direction: if the scheme is both consistent and stable, then the scheme is convergent. However, since this ...
194 views

### Converge rate analysis: issue with time convergence

I have written a code which solves the incompressible formulation of the Navier-Stokes equations. It uses high-order methods both for time and spatial derivatives. I have been conducting convergence ...
262 views

### Non-monotonic convergence in fixed-point problem

Background I am solving a variant of the Ornstein-Zernike equation from liquid theory. Abstractly, the problem can be represented as solving the fixed point problem $A c(r)=c(r)$, where $A$ is an ...
383 views