TY - GEN
T1 - First-Order System Least Squares Finite-Elements for Singularly Perturbed Reaction-Diffusion Equations
AU - Adler, James H.
AU - MacLachlan, Scott
AU - Madden, Niall
N1 - Publisher Copyright:
© 2020, Springer Nature Switzerland AG.
PY - 2020
Y1 - 2020
N2 - We propose a new first-order-system least squares (FOSLS) finite-element discretization for singularly perturbed reaction-diffusion equations. Solutions to such problems feature layer phenomena, and are ubiquitous in many areas of applied mathematics and modelling. There is a long history of the development of specialized numerical schemes for their accurate numerical approximation. We follow a well-established practice of employing a priori layer-adapted meshes, but with a novel finite-element method that yields a symmetric formulation while also inducing a so-called “balanced” norm. We prove continuity and coercivity of the FOSLS weak form, present a suitable piecewise uniform mesh, and report on the results of numerical experiments that demonstrate the accuracy and robustness of the method.
AB - We propose a new first-order-system least squares (FOSLS) finite-element discretization for singularly perturbed reaction-diffusion equations. Solutions to such problems feature layer phenomena, and are ubiquitous in many areas of applied mathematics and modelling. There is a long history of the development of specialized numerical schemes for their accurate numerical approximation. We follow a well-established practice of employing a priori layer-adapted meshes, but with a novel finite-element method that yields a symmetric formulation while also inducing a so-called “balanced” norm. We prove continuity and coercivity of the FOSLS weak form, present a suitable piecewise uniform mesh, and report on the results of numerical experiments that demonstrate the accuracy and robustness of the method.
KW - First-order system least squares (FOSLS) finite elements
KW - Parameter-robust discretizations
KW - Singularly perturbed differential equations
UR - https://www.scopus.com/pages/publications/85081121416
U2 - 10.1007/978-3-030-41032-2_1
DO - 10.1007/978-3-030-41032-2_1
M3 - Conference Publication
SN - 9783030410315
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 3
EP - 14
BT - Large-Scale Scientific Computing - 12th International Conference, LSSC 2019, Revised Selected Papers
A2 - Lirkov, Ivan
A2 - Margenov, Svetozar
PB - Springer
T2 - 12th International Conference on Large-Scale Scientific Computing, LSSC 2019
Y2 - 10 June 2019 through 14 June 2019
ER -