Volume 7, Issue 3
Parabolic Singularly Perturbed Problems with Exponential Layers: Robust Discretizations Using Finite Elements in Space on Shishkin Meshes

Int. J. Numer. Anal. Mod., 7 (2010), pp. 593-606

Published online: 2010-07

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• Abstract
A parabolic initial-boundary value problem with solutions displaying exponential layers is solved using layer-adapted meshes. The paper combines finite elements in space, i.e., a pure Galerkin technique on a Shishkin mesh, with some standard discretizations in time. We prove error estimates as well for the $theta$-scheme as for discontinuous Galerkin in time.
• Keywords

Convection-diffusion transient finite element Shishkin mesh time discretization

65N12 65N30 65N50

@Article{IJNAM-7-593, author = {L. Kaland and H.-G. Roos}, title = {Parabolic Singularly Perturbed Problems with Exponential Layers: Robust Discretizations Using Finite Elements in Space on Shishkin Meshes}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2010}, volume = {7}, number = {3}, pages = {593--606}, abstract = {A parabolic initial-boundary value problem with solutions displaying exponential layers is solved using layer-adapted meshes. The paper combines finite elements in space, i.e., a pure Galerkin technique on a Shishkin mesh, with some standard discretizations in time. We prove error estimates as well for the $theta$-scheme as for discontinuous Galerkin in time.}, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/740.html} }
TY - JOUR T1 - Parabolic Singularly Perturbed Problems with Exponential Layers: Robust Discretizations Using Finite Elements in Space on Shishkin Meshes AU - L. Kaland & H.-G. Roos JO - International Journal of Numerical Analysis and Modeling VL - 3 SP - 593 EP - 606 PY - 2010 DA - 2010/07 SN - 7 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/740.html KW - Convection-diffusion KW - transient KW - finite element KW - Shishkin mesh KW - time discretization AB - A parabolic initial-boundary value problem with solutions displaying exponential layers is solved using layer-adapted meshes. The paper combines finite elements in space, i.e., a pure Galerkin technique on a Shishkin mesh, with some standard discretizations in time. We prove error estimates as well for the $theta$-scheme as for discontinuous Galerkin in time.