The Nørsett time integration methodology for finite element transient analysis Original Research Article

This paper presents a set of methods for time integration of problems arising from finite element semidiscretizations. The purpose is to obtain computationally efficient methods which possess higher-order accuracy and controllable dissipation in the spurious high modes. The methods are developed and analysed by a general collocation methodology which leads to the class of Nørsett approximants. An algorithmic parameter is used to achieve an effective control over numerical dissipation. Moreover, a simple and efficient implementation scheme is presented. At each time step, algorithms based on p-order collocation polynomials require the solution of p sets of linear algebraic equations with the same coefficient matrix. In this way, a single factorization is needed and no transformations are required to recover the approximate solution at the end or within the time interval. To demonstrate the performance of the proposed algorithms, a wide experimental evaluation is carried out on typical test problems in finite element transient analysis.