Projection-free approximation of geometrically constrained partial differential equations

Bartels, Sören

doi:10.1090/mcom/3008

Projection-free approximation of geometrically constrained partial differential equations
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Math. Comp. 85 (2016), 1033-1049 Request permission

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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