TY - GEN
T1 - Numerical analysis of a 2D singularly perturbed semilinear reaction-diffusion problem
AU - Kopteva, Natalia
PY - 2009
Y1 - 2009
N2 - A semilinear reaction-diffusion equation with multiple solutions is considered in a smooth two-dimensional domain. Its diffusion parameter ε2 is arbitrarily small, which induces boundary layers. We extend the numerical method and its maximum norm error analysis of the paper [N. Kopteva: Math. Comp. 76 (2007) 631-646], in which a parametrization of the boundary δω is assumed to be known, to a more practical case when the domain is defined by an ordered set of boundary points. It is shown that, using layer-adapted meshes, one gets secondorder convergence in the discrete maximum norm, uniformly in ε for ε ≤ Ch. Here h > 0 is the maximum side length of mesh elements, while the number of mesh nodes does not exceed Ch-2. Numerical results are presented that support our theoretical error estimates.
AB - A semilinear reaction-diffusion equation with multiple solutions is considered in a smooth two-dimensional domain. Its diffusion parameter ε2 is arbitrarily small, which induces boundary layers. We extend the numerical method and its maximum norm error analysis of the paper [N. Kopteva: Math. Comp. 76 (2007) 631-646], in which a parametrization of the boundary δω is assumed to be known, to a more practical case when the domain is defined by an ordered set of boundary points. It is shown that, using layer-adapted meshes, one gets secondorder convergence in the discrete maximum norm, uniformly in ε for ε ≤ Ch. Here h > 0 is the maximum side length of mesh elements, while the number of mesh nodes does not exceed Ch-2. Numerical results are presented that support our theoretical error estimates.
UR - http://www.scopus.com/inward/record.url?scp=67650468397&partnerID=8YFLogxK
U2 - 10.1007/978-3-642-00464-3_8
DO - 10.1007/978-3-642-00464-3_8
M3 - Conference contribution
AN - SCOPUS:67650468397
SN - 3642004636
SN - 9783642004636
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 80
EP - 91
BT - Numerical Analysis and Its Applications - 4th International Conference, NAA 2008, Revised Selected Papers
PB - Springer Verlag
T2 - 4th International Conference on Numerical Analysis and Its Applications, NAA 2008
Y2 - 16 June 2008 through 20 June 2008
ER -