The H and P methods are two different approaches used in finite element method (FEM) for approximating solutions to partial differential equations (PDEs). The main difference between these two methods lies in the way in which the solution is discretized.
The accuracy of the H and P methods depends on the specific problem being solved. In general, the P method is more accurate as it allows for a higher order polynomial approximation of the solution, resulting in a more accurate representation of the PDE. However, the H method can also achieve high accuracy by using a finer mesh.
The H method is advantageous because it is simpler to implement and requires less computational resources compared to the P method. It is also more robust in handling problems with irregular geometries or material properties.
The P method should be used when high accuracy is required, or when the solution has high gradients or discontinuities. It is also more suitable for problems with smooth and regular geometries.
Yes, the H and P methods can be combined to take advantage of their individual strengths. This is known as the hp-FEM, where the mesh is refined in certain regions using the H method and in other regions using the P method. This allows for a more efficient and accurate solution for complex problems.