A stable space-time FEM in loving memory of Prof. Allotey
In memory of the man who bought a flight ticket that changed my life.
After his passing away, i thought of an appropriate way to show my appreciation for the enormous assistance he gave to me. In my earlier article, i narrated the story of how he bought my flight ticket when i least could afford it. It was this gesture that enabled me to pursue graduate studies and finally post-graduate studies.
Prof. Allotey was a mathematical physicist and as such the titled article "A stable space-time FEM for parabolic evolution problems" is befitting to his memory. Published in Calcolo which is under the direction of the Institute for Informatics and Telematics in Pisa because Allotey served as a member of the scientific council of ICTP, Italy for many years. The paper is already online and available for paid paying members.
A stable space–time finite element method for parabolic evolution problems There's however a copy freely available with minor corrections compared to the published one also on arXiv and researchgate with the same title. This is for those with limited to no access to Springer's jorunals.
In this paper, we discuss an on-going development in computational science on the topic of space-time continuum where the time dimension is considered as an extension of the spatial dimension. This is popularly referred to as the space-time continuum. Thus, it is possible to solve and analyse time-dependent problems by avoiding the traditional time-stepping schemes. This idea coupled with current advancement in computing technologies makes the future of solving time-dependent problems very exciting from both the physics and mathematics point of view.