Picture of two heads

Open Access research that challenges the mind...

The Strathprints institutional repository is a digital archive of University of Strathclyde research outputs. Strathprints provides access to thousands of Open Access research papers by University of Strathclyde researchers, including those from the School of Psychological Sciences & Health - but also papers by researchers based within the Faculties of Science, Engineering, Humanities & Social Sciences, and from the Strathclyde Business School.

Discover more...

Implicit solution of hyperbolic equations with space-time adaptivity

Lötstedt, P. and Ramage, A. and Hemmingsson-Frändén, L. and Söderberg, S. (2002) Implicit solution of hyperbolic equations with space-time adaptivity. BIT Numerical Mathematics, 42 (1). pp. 134-158. ISSN 0006-3835

Full text not available in this repository. (Request a copy from the Strathclyde author)

Abstract

Adaptivity in space and time is introduced to control the error in the numerical solution of hyperbolic partial differential equations. The equations are discretised by a finite volume method in space and an implicit linear multistep method in time. The computational grid is refined in blocks. At the boundaries of the blocks, there may be jumps in the step size. Special treatment is needed there to ensure second order accuracy and stability. The local truncation error of the discretisation is estimated and is controlled by changing the step size and the time step. The global error is obtained by integration of the error equations. In the implicit scheme, the system of linear equations at each time step is solved iteratively by the GMRES method. Numerical examples executed on a parallel computer illustrate the method.