Finite Element Analysis
DOI link for Finite Element Analysis
Finite Element Analysis book
Finite element analysis is a numerical technique for solving differential equations. It involves discretization of a region of interest into many meshes or elements. The task of finite element analysis is to determine the nodal values. A common practice in finite element analysis is to weight the error over an entire element before minimizing the residual. The lumped formulation has the advantage of less numerical oscillation during matrix inversion as compared to the consistent formulation. In addition to the inherent error in the finite-element approximation to the differential equation, there are errors associated with hardware and software. Because of the finite precision in digital representation of variables, round-off error occurs during computation. Numerical instability refers to the amplification of errors when equation solving proceeds from one time step to the next. Numerical oscillations may occur when steep gradients across temperature or concentration fronts are simulated.