A \(C^ 1\) finite element collocation method for the equations of one- dimensional nonlinear thermoviscoelasticity (Q1122418)

The paper deals with the solution of the equations of one-dimensional nonlinear thermoelasticity and employs a finite element collocation method at Gaussian points based on the use of a function space consisting of \(C^ 1\) piecewise polynomials of degree \(\leq r\), where \(r\geq 3\) for approximation in the space variable and a three level difference scheme for approximation in the time variable. The displacement gradient u and the temperature difference \(\theta\) are computed at each time step separately and this results in computational economy. Bounds on the error are derived. The hypotheses in the paper are more stringent than those in the scheme using the finite element method, as the approximate solutions are to satisfy the differential equations exactly at the collocation points and not in an average sense through integrals.