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Mesh refinement and convergence

The FEM solution approaches the exact solution as elements are made smaller (h-refinement) or the polynomial degree is raised (p-refinement). A convergence study compares the result at different mesh densities to check that the answer no longer changes much.

\text{Error} \propto h^{p+1}

displacement error, element degree

p

Symbols

$h$	element size	m
$p$	polynomial degree

Example

Linear elements ( $p=1$ ), element size halved:

the error is reduced by a factor of $2^2 = 4$ .

Put the finest elements where the stress gradients are largest, not evenly over the whole model.

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Part of Finite Element Method: Element types, meshing and error.