A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
نویسندگان
چکیده
منابع مشابه
A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
In this work we deal with the Dirichlet homogeneous problem for the integral fractional Laplacian on a bounded domain Ω ⊂ R. Namely, we deal with basic analytical aspects required to convey a complete Finite Element analysis of the problem (1) { (−∆)u = f in Ω, u = 0 in Ω, where the fractional Laplacian of order s is defined by (−∆)u(x) = C(n, s) P.V. ∫ Rnu(x)− u(y)|x− y|n+2s dyand ...
متن کاملWeak and Viscosity Solutions of the Fractional Laplace Equation
Aim of this paper is to show that weak solutions of the following fractional Laplacian equation { (−∆)su = f in Ω u = g in Rn \ Ω are also continuous solutions (up to the boundary) of this problem in the viscosity sense. Here s ∈ (0, 1) is a fixed parameter, Ω is a bounded, open subset of Rn (n > 1) with C2-boundary, and (−∆)s is the fractional Laplacian operator, that may be defined as (−∆)u(x...
متن کاملRegularity of Solutions to a Time-Fractional Diffusion Equation
The paper proves estimates for the partial derivatives of the solution to a time-fractional diffusion equation, posed over a bounded spatial domain. Such estimates are needed for the analysis of effective numerical methods, particularly since the solution is less regular than in the well-known case of classical diffusion.
متن کاملFinite difference approximations for a fractional diffusion/anti-diffusion equation
A class of finite difference schemes for solving a fractional anti-diffusive equation, recently proposed by Andrew C. Fowler to describe the dynamics of dunes, is considered. Their linear stability is analyzed using the standard Von Neumann analysis: stability criteria are found and checked numerically. Moreover, we investigate the consistency and convergence of these schemes.
متن کاملFinite Element Approximations of the Nonhomogeneous Fractional Dirichlet Problem
We study finite element approximations of the nonhomogeneous Dirichlet problem for the fractional Laplacian. Our approach is based on weak imposition of the Dirichlet condition and incorporating a nonlocal analogous of the normal derivative as a Lagrange multiplier in the formulation of the problem. In order to obtain convergence orders for our scheme, regularity estimates are developed, both f...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: SIAM Journal on Numerical Analysis
سال: 2017
ISSN: 0036-1429,1095-7170
DOI: 10.1137/15m1033952