A computerized process for defining finite elements in a surface or volume for ultimately predicting a physical characteristic of the surface or volume. For the surface, for example, the process includes a first step of inputting surface boundary point coordinates of a geometric model of the surface to a computer system, the computer system including an image display screen displaying the geometric model. The process further includes preparing the boundary edges of surface by generating piecewise geometrically smooth bezier curves between boundary points and converting the bezier curves to cubic interpolation polynomials and defining evenly spaced points on each cubic interpolation polynomial and decomposing the surface with divider curves, if the surface is not already 3, 4, or 5 sided, into 3, 4, and 5 sided primitives. Thereafter, a determination is made of the largest acceptable element size and the number of elements disposed along each edge of each primitive. The next steps are readjusting one of the divider curves to match a closest even element vertices and mapping in 3 and 5 sided clusters and then preparing remaining 4 sided primitives for decomposition into 4 sided elements and mapping in elements and element patches. Thereafter, method includes the steps of optimising the elements in the mesh and writing the resulting mesh to a storage file.