TY - GEN
T1 - Improved energy-norm a posteriori error estimates for singularly perturbed reaction-diffusion problems on anisotropic meshes
AU - Kopteva, Natalia
N1 - Publisher Copyright:
© Springer Nature Switzerland AG 2020.
PY - 2020
Y1 - 2020
N2 - In the recent article (Kopteva, Numer Math 137:607–642, 2017) the author obtained residual-type a posteriori error estimates in the energy norm for singularly perturbed semilinear reaction-diffusion equations on unstructured anisotropic triangulations. The error constants in these estimates are independent of the diameters and the aspect ratios of mesh elements and of the small perturbation parameter. The purpose of this note is to improve the weights in the jump residual part of the estimator. This is attained by using a novel sharper version of the scaled trace theorem for anisotropic elements, in which the hat basis functions are involved as weights.
AB - In the recent article (Kopteva, Numer Math 137:607–642, 2017) the author obtained residual-type a posteriori error estimates in the energy norm for singularly perturbed semilinear reaction-diffusion equations on unstructured anisotropic triangulations. The error constants in these estimates are independent of the diameters and the aspect ratios of mesh elements and of the small perturbation parameter. The purpose of this note is to improve the weights in the jump residual part of the estimator. This is attained by using a novel sharper version of the scaled trace theorem for anisotropic elements, in which the hat basis functions are involved as weights.
UR - http://www.scopus.com/inward/record.url?scp=85089718008&partnerID=8YFLogxK
U2 - 10.1007/978-3-030-41800-7_9
DO - 10.1007/978-3-030-41800-7_9
M3 - Conference contribution
AN - SCOPUS:85089718008
SN - 9783030417994
T3 - Lecture Notes in Computational Science and Engineering
SP - 143
EP - 156
BT - Boundary and Interior Layers, Computational and Asymptotic Methods, BAIL 2018
A2 - Barrenechea, Gabriel R.
A2 - Mackenzie, John
PB - Springer
T2 - International Conference on Boundary and Interior Layers, BAIL 2018
Y2 - 18 June 2018 through 22 June 2018
ER -