The Stochastic Finite Element Method for Nuclear Applications

Mena, J.D. Arregui; Margetts, Lee; Evans, Llion; Griffiths, D. V.; Shterenlikht, Anton; Cebamanos, Luis; Mummery, Paul

doi:10.7712/100016.1975.9348

Search citation statements

Order By: Relevance

Paper Sections

Select...

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2017

2019

Publication Types

Select...

Article1

Other1

Relationship

Self Cite0

Independent2

Authors

Journals

Cited by 2 publications

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

Energy-corrected FEM and explicit time-stepping for parabolic problems

Swierczynski

Wohlmuth

2019

ESAIM: M2AN

View full text Add to dashboard Cite

The presence of corners in the computational domain, in general, reduces the regularity of solutions of parabolic problems and diminishes the convergence properties of the finite element approximation introducing a so-called "pollution effect". Standard remedies based on mesh refinement around the singular corner result in very restrictive stability requirements on the time-step size when explicit time integration is applied. In this article, we introduce and analyse the energy-corrected finite element method for parabolic problems, which works on quasi-uniform meshes, and, based on it, create fast explicit time discretisation. We illustrate these results with extensive numerical investigations not only confirming the theoretical results but also showing the flexibility of the method, which can be applied in the presence of multiple singular corners and a three-dimensional setting. We also propose a fast explicit time-stepping scheme based on a piecewise cubic energy-corrected discretisation in space completed with mass-lumping techniques and numerically verify its efficiency.

show abstract