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Mathematics of Computation

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Projection-free approximation of geometrically constrained partial differential equations

Author: Sören Bartels
Journal: Math. Comp. 85 (2016), 1033-1049
MSC (2010): Primary 65N12; Secondary 65N15, 65N30
Published electronically: July 21, 2015
MathSciNet review: 3454357
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Abstract: We devise algorithms for the numerical approximation of partial differential equations involving a nonlinear, pointwise holonomic constraint. The elliptic, parabolic, and hyperbolic model equations are replaced by sequences of linear problems with a linear constraint. Stability and convergence hold unconditionally with respect to step sizes and triangulations. In the stationary situation a multilevel strategy is proposed that iteratively decreases the step size. Numerical experiments illustrate the accuracy of the approach.

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Additional Information

Sören Bartels
Affiliation: Department of Applied Mathematics, Mathematical Institute, University of Freiburg, Hermann-Herder-Str 9, 79104 Freiburg i. Br., Germany

Keywords: Finite elements, partial differential equations, pointwise constraints, harmonic maps, harmonic map heat flow, wave maps
Received by editor(s): August 20, 2013
Received by editor(s) in revised form: April 7, 2014, and October 21, 2014
Published electronically: July 21, 2015
Article copyright: © Copyright 2015 American Mathematical Society