We know that the solution we obtain from Finite Element Analysis is always an approximate one and not exact. However, it is possible to reduce error to a minimum acceptable level. When this happens, we say that solution converges.
To ensure convergence following criteria have to be fulfilled. These criteria pertain to the polynomial which we assume to be the approximate solution to the problem in hand.
- Polynomial should be a complete polynomial i.e it must contain all the degree from 0 to the highest order of the derivative used in weak form. This requirement is necessary to capture all possible states of the actual solution.
- The polynomial should be contineous over the element and also differentiable upto the order of the derivatives in the weak form.This requirement ensures non-zero coefficients in the solutions.
- The approximate solution should be interpolation function of the primary variables at the nodes of the finite element. This requirement is essential to ensure compatibility of the solution.
Besides these criteria, we can improve upon convergence by reducing the size of the elements i.e increasing number of elements in which case we call h-cenvergence or by increasing the degree of polynomial in which case we call p-convergence.