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Convergence in COMSOL Multiphysics

What exactly is "Convergence"?

Convergence in COMSOL Multiphysics: Convergence is defined as the process of arriving at a solution that is very near to the precise answer within some error tolerance or other convergence condition that was previously set.


Why would you need to compute the solution in COMSOL if you already know the precise answer to the problem?
You are missing the main issue, which is that you do not know the specific answer. However, you are able to make an estimate of the error that is associated with your numerical solution, which is always an approximation. You may, for instance, reintroduce the numerical values into the equations and check to see how well they match up. Your numerical solution has met the numerical convergence criteria if it matches within an acceptable range (relative tolerance, for example, an error of 0.1 percent), such as when it matches within 0.1 percent.
Please find attached a figure showing the convergence of a calculation for a nonlinear model (created automatically in COMSOL).
The concept of "mesh convergence" is another essential one. Your solution is considered to be mesh convergent if the findings are not materially altered by applying a global or local mesh refinement. Your objective should be to construct a mesh that just satisfies mesh convergence but is not finer than is required in order to keep the computational cost as low as feasible. This will allow for the most economical modeling possible.

Convergence Plots

Convergence plots use graphics to show how an error estimate or time step evolves during the solution process for nonlinear, time-dependent, and parametric solvers. By default, convergence plots are generated.

The convergence plots show an error estimate against the iteration number for the nonlinear solver and for the iterative linear system solvers (the Conjugate gradients, BiCGStab, GMRES, FGMRES, TFQMR, and multigrid solvers)

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