Convergence, Accuracy, and Stability of Finite-Element Approximations of a Class of Nonlinear Hyperbolic Equations

摘要

Numerical stability criteria and rates of convergence are derived for finite-element approximations of the nonlinear wave equation (u sub tt) - F (u sub x) = f(x,t), where F (u sub x) possesses properties generally encountered in nonlinear elasticity. Piecewise linear finite-element approximations in x and central difference approximations in t are studied. (Author)