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Mathematics of Computation

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Numerical approximation of planar oblique derivative problems in nondivergence form

Author: Dietmar Gallistl
Journal: Math. Comp. 88 (2019), 1091-1119
MSC (2010): Primary 65N12, 65N15, 65N30
Published electronically: July 23, 2018
MathSciNet review: 3904140
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Abstract: A numerical method for approximating a uniformly elliptic oblique derivative problem in two-dimensional simply-connected domains is proposed. The numerical scheme employs a mixed formulation with piecewise affine functions on curved finite element domains. The direct approximation of the gradient of the solution turns the oblique derivative boundary condition into an oblique direction condition. A priori and a posteriori error estimates as well as numerical computations on uniform and adaptive meshes are provided.

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Additional Information

Dietmar Gallistl
Affiliation: Department of Applied Mathematics, University of Twente, 7500 AE Enschede, The Netherlands

Keywords: Oblique derivative problem, nondivergence form, Cordes coefficents, a priori error analysis, a posteriori error analysis
Received by editor(s): November 28, 2017
Received by editor(s) in revised form: February 27, 2018, and April 15, 2018
Published electronically: July 23, 2018
Additional Notes: The author was supported by the Deutsche Forschungsgemeinschaft (DFG) through CRC 1173.
Article copyright: © Copyright 2018 American Mathematical Society