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dc.contributor.authorHuang, Weizhang
dc.contributor.authorKamenski, Lennard
dc.contributor.authorLang, Jens
dc.date.accessioned2017-11-10T18:02:53Z
dc.date.available2017-11-10T18:02:53Z
dc.date.issued2016-05-26
dc.identifier.citationHuang, W., Kamenski, L., & Lang, J. (2016). Stability of Explicit One-Step Methods for P1-Finite Element Approximation of Linear Diffusion Equations on Anisotropic Meshes. SIAM Journal on Numerical Analysis, 54(3), 1612-1634. doi:10.1137/130949531en_US
dc.identifier.urihttp://hdl.handle.net/1808/25322
dc.descriptionThe research of the authors was supported in part by the NSF (USA) under grant DMS-1115118, the DFG (Germany) under grant KA 3215/2-1, and the Darmstadt Graduate Schools of Excellence Computational Engineering and Energy Science and Engineering.en_US
dc.description.abstractWe study the stability of explicit one-step integration schemes for the linear finite element approximation of linear parabolic equations. The derived bound on the largest permissible time step is tight for any mesh and any diffusion matrix within a factor of $2(d+1)$, where $d$ is the spatial dimension. Both full mass matrix and mass lumping are considered. The bound reveals that the stability condition is affected by two factors. The first depends on the number of mesh elements and corresponds to the classic bound for the Laplace operator on a uniform mesh. The second factor reflects the effects of the interplay of the mesh geometry and the diffusion matrix. It is shown that it is not the mesh geometry itself but the mesh geometry in relation to the diffusion matrix that is crucial to the stability of explicit methods. When the mesh is uniform in the metric specified by the inverse of the diffusion matrix, the stability condition is comparable to the situation with the Laplace operator on a uniform mesh. Numerical results are presented to verify the theoretical findings.en_US
dc.publisherSociety for Industrial and Applied Mathematicsen_US
dc.rights© 2016, Society for Industrial and Applied Mathematicsen_US
dc.subjectFinite element methoden_US
dc.subjectAnisotropic meshen_US
dc.subjectStability conditionen_US
dc.subjectParabolic equationen_US
dc.subjectExplicit one-step methoden_US
dc.titleStability of Explicit One-Step Methods for P1-Finite Element Approximation of Linear Diffusion Equations on Anisotropic Meshesen_US
dc.typeArticleen_US
kusw.kuauthorHuang, Weizhang
kusw.kudepartmentMathematicsen_US
dc.identifier.doi10.1137/130949531en_US
kusw.oaversionScholarly/refereed, publisher versionen_US
kusw.oapolicyThis item meets KU Open Access policy criteria.en_US
dc.rights.accessrightsopenAccess


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