The major advantages of the FEM over FDM and FVM are its built-in abilities to handle unstructured meshes, a rich family of element choices, and natural handling of BOUNDARY conditions (especially flux relations). The FDM is generally restricted to simple geometries in which an orthogonal grid can be constructed; for IRREGULAR geometries, a global transformation of the governing equations (e.g., boundary fitted coordinates) must be MADE to create an orthogonal COMPUTATIONAL domain. Likewise, implementation of boundary conditions in FDM can be cumbersome. The FVM is an integral approach (typically with limits -0.5 to 0.5) similar to the FEM, with volumes being used instead of elements. The divergence theorem is used to establish the final equation set. Solutions are obtained at volume faces, VERTICES, or volume centers – some methods employ staggered grids. While FVM can handle irregular domains using unstructured grids (stemming from the FEM), the required averaging over the volume limits the method to second order spatial accuracy.

The major advantages of the FEM over FDM and FVM are its built-in abilities to handle unstructured meshes, a rich family of element choices, and natural handling of boundary conditions (especially flux relations). The FDM is generally restricted to simple geometries in which an orthogonal grid can be constructed; for irregular geometries, a global transformation of the governing equations (e.g., boundary fitted coordinates) must be made to create an orthogonal computational domain. Likewise, implementation of boundary conditions in FDM can be cumbersome. The FVM is an integral approach (typically with limits -0.5 to 0.5) similar to the FEM, with volumes being used instead of elements. The divergence theorem is used to establish the final equation set. Solutions are obtained at volume faces, vertices, or volume centers – some methods employ staggered grids. While FVM can handle irregular domains using unstructured grids (stemming from the FEM), the required averaging over the volume limits the method to second order spatial accuracy.