6 papers · 1 filter
A finite difference scheme for two-dimensional singularly perturbed convection-diffusion problem with discontinuous source term
Ram Shiromani, Niall Madden, V. Shanthi
We propose a finite difference scheme for the numerical solution of a two-dimensional singularly perturbed convection-diffusion partial differential equation whose solution feature…
Layer-adapted meshes for singularly perturbed problems via mesh partial differential equations and a posteriori information
Róisín Hill, Niall Madden
We propose a new method for the construction of layer-adapted meshes for singularly perturbed differential equations (SPDEs), based on mesh partial differential equations (MPDEs) t…
A Boundary-Layer Preconditioner for Singularly Perturbed Convection Diffusion
Scott P. MacLachlan, Niall Madden, Thái Anh Nhan
Motivated by a wide range of real-world problems whose solutions exhibit boundary and interior layers, the numerical analysis of discretizations of singularly perturbed differentia…
First-order system least squares finite-elements for singularly perturbed reaction-diffusion equations
James H. Adler, Scott MacLachlan, Niall Madden
We propose a new first-order-system least squares (FOSLS) finite-element discretization for singularly perturbed reaction-diffusion equations. Solutions to such problems feature la…
An introduction to the analysis and implementation of sparse grid finite element methods
Stephen Russell, Niall Madden
Our goal is to present an elementary approach to the analysis and programming of sparse grid finite element methods. This family of schemes can compute accurate solutions to partia…
Cholesky factorisation of linear systems coming from finite difference approximations of singularly perturbed problems
Thái Anh Nhan, Niall Madden
We consider the solution of large linear systems of equations that arise when two-dimensional singularly perturbed reaction-diffusion equations are discretized. Standard methods fo…