Finite element algorithms for nonlocal minimal graphs
Copyright policy )Finite element algorithms for nonlocal minimal graphs
<abstract><p>We discuss computational and qualitative aspects of the fractional Plateau and the prescribed fractional mean curvature problems on bounded domains subject to exterior data being a subgraph. We recast these problems in terms of energy minimization, and we discretize the latter with piecewise linear finite elements. For the computation of the discrete solutions, we propose and study a gradient flow and a Newton scheme, and we quantify the effect of Dirichlet data truncation. We also present a wide variety of numerical experiments that illustrate qualitative and quantitative features of fractional minimal graphs and the associated discrete problems.</p></abstract>
- University of Maryland, College Park United States
- University of the Republic Uruguay
- University of Tennessee at Knoxville United States
- THE UNIVERSITY OF TENNESSEE United States
T57-57.97, Numerical optimization and variational techniques, Applied mathematics. Quantitative methods, Finite elements, fractional diffusion, nonlocal minimal surfaces, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, PDEs on graphs and networks (ramified or polygonal spaces), Fractional partial differential equations, Nonlocal minimal surfaces, Fractional derivatives and integrals, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, 49Q05, 35R11, 65N12, 65N30, finite elements, Fractional diffusion, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
T57-57.97, Numerical optimization and variational techniques, Applied mathematics. Quantitative methods, Finite elements, fractional diffusion, nonlocal minimal surfaces, Existence problems for PDEs: global existence, local existence, non-existence, Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness, Numerical Analysis (math.NA), Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs, PDEs on graphs and networks (ramified or polygonal spaces), Fractional partial differential equations, Nonlocal minimal surfaces, Fractional derivatives and integrals, Finite difference methods for initial value and initial-boundary value problems involving PDEs, FOS: Mathematics, 49Q05, 35R11, 65N12, 65N30, finite elements, Fractional diffusion, Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs, Mathematics - Numerical Analysis, Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
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