Finite element method and some applications

The region R is subdivided into discrete subregions or elements (triangles), with the boundaries of each element being plane or curvilinear faces, and with the adjacent boundaries of any pair of elements being coincident. A trial solution of the form = y- 0r(x^i)Cr is used with an extremal principle for r=l each element, to obtain a set of equations from which the unknown parameters Cr are determined. If we solve the equations Ax = b, via the standard symmetric factorization of A, then 0(n^4) arithmetic operations are required if the usual row by row numbering scheme is used, and storage required 0(n^3). If we avoid operating on zeros, the LDL^T factorization of A can be computed using the same standard algorithm in 0(n3) arithmetic operations. Furthermore, the storage required is only 0(n^2log2n).