p-method means that you use higher order shape functions to describe your problems. The convergence is much higher and you need less degrees of freedom. However, the numcerical cost to create your elements is higher.
h-method means standard FEM. You try to approximate your solution with a large number of lower order elements.
To approximate a arbitrary function you can use a lot of small linear functions. If the length goes to zero your approxiation is exact. The other way is you increase your polynomial order. Also then you will get a better solution for larger orders.
p-method means that you use higher order shape functions to describe your problems. The convergence is much higher and you need less degrees of freedom. However, the numcerical cost to create your elements is higher.
h-method means standard FEM. You try to approximate your solution with a large number of lower order elements.
To approximate a arbitrary function you can use a lot of small linear functions. If the length goes to zero your approxiation is exact. The other way is you increase your polynomial order. Also then you will get a better solution for larger orders.
In practice, the p-method is obsolete and only linear (I-order) and parabolic (II-order) shape function/elements are in use.
Instead, a h-method is widely used and partially automated by many algorithms of the mesh adaptation (a local mesh refinement) based for example on the local stress gradient. This tool is available in almost all commercial FEM codes.
I have added a Technical Report (see below) which shows an example of 'p'-type and 'h'-type refinement for a practical engineering problem which might provide some assistance in answering this question.
https://www.researchgate.net/publication/264239733_%27p%27-type_or_%27h%27-type_Elements?ev=prf_pub
Technical Report 'p'-type or 'h'-type Elements?
Simple is that if you consider computational domain of a single element with more points you need a higher order polynomial to interpolate them with p-method. The same domain/element can be decretised with more number of elements using h-method.
- Badges
- Science topic