Which method is utilized to increase the polynomial order of mesh elements?

The P-method is used to increase the polynomial order of mesh elements in finite element analysis. This technique enhances the accuracy of the solution by refining the representation of the solution within each element, rather than changing the mesh configuration itself. By increasing the polynomial order, the elements can capture more complex behavior and gradients within the material they represent.

For example, if the mesh elements are initially linear, applying the P-method can transition them to quadratic or cubic elements. This allows for a more precise approximation of the solution, particularly in regions where there are high gradients or nonlinear behavior. Therefore, the P-method is particularly beneficial in simulations requiring higher fidelity in results without the need for a significantly denser mesh, which could increase computational costs.

In contrast, while other methods, such as the H-method, focus on refining the mesh density itself by adding more elements, the P-method aims directly at enhancing the polynomial degree within the existing mesh structure. This distinction makes the P-method the appropriate choice for increasing the polynomial order of mesh elements.