A Convergent and Constraint-Preserving Finite Element Method for the p-Harmonic Flow into Spheres
نویسندگان
چکیده
An explicit fully discrete finite element method, which satisfies the nonconvex side constraint at every node, is developed for approximating the p-harmonic flow for p ∈ (1,∞). Convergence of the method is established under certain conditions on the domain and mesh. Computational examples are presented to demonstrate finite-time blow-ups and qualitative geometric changes of weak solutions of the p-harmonic flow.
منابع مشابه
Constraint preserving implicit finite element discretization of harmonic map flow into spheres
Discretization of the harmonic map flow into spheres often uses a penalization or projection strategy, where the first suffers from the proper choice of an additional parameter, and the latter from the lack of a discrete energy law, and restrictive mesh-constraints. We propose an implicit scheme that preserves the sphere constraint at every node, enjoys a discrete energy law, and unconditionall...
متن کاملConvergent discretization of heat and wave map flows to spheres using approximate discrete Lagrange multipliers
We propose fully discrete schemes to approximate the harmonic map heat flow and wave maps into spheres. The finite-element based schemes preserve a unit length constraint at the nodes by means of approximate discrete Lagrange multipliers, satisfy a discrete energy law, and iterates are shown to converge to weak solutions of the continuous problem. Comparative computational studies are included ...
متن کاملOn p-Harmonic Map Heat Flows for 1<=p<∞ and Their Finite Element Approximations
Motivated by emerging applications from imaging processing, the heat flow of a generalized p-harmonic map into spheres is studied for the whole spectrum, 1 ≤ p <∞, in a unified framework. The existence of global weak solutions is established for the flow using the energy method together with a regularization and a penalization technique. In particular, a BV -solution concept is introduced and t...
متن کاملFast and Accurate Finite Element Approximation of Wave Maps into Spheres
A constraint preserving numerical method for the approximation of wave maps into spheres is presented. The scheme has a second order consistency property and is energy preserving and reversible. Its unconditional convergence to an exact solution is proved. A fixed point iteration allows for a solution of the nonlinear system of equations in each time step under a moderate step size restriction.
متن کاملGalerkin Finite-Element Method for the Analysis of the Second Harmonic Generation in Wagon Wheel Fibers
The nonlinear effects of the second harmonic generation have been investigated for the propagation of light along the axis of fibers of wagon wheel cross sectional shape. Nodal finite element formulation is utilized to obtain discretized Helmholtz equations under appropriate boundary conditions. The hierarchical p-version nodal elements are used for meshing the cross section of wagon wheel fibe...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- SIAM J. Numerical Analysis
دوره 45 شماره
صفحات -
تاریخ انتشار 2007