Local Energy Estimates for the Fractional Laplacian
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Publication:5001382
DOI10.1137/20M1335509zbMath1486.65240arXiv2005.03786OpenAlexW3181328114MaRDI QIDQ5001382
Dmitriy Leykekhman, Juan Pablo Borthagaray, Ricardo H. Nochetto
Publication date: 19 July 2021
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.03786
Error bounds for boundary value problems involving PDEs (65N15) Fractional derivatives and integrals (26A33) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Fractional partial differential equations (35R11)
Related Items (13)
A Monotone Discretization for Integral Fractional Laplacian on Bounded Lipschitz Domains: Pointwise Error Estimates under Hölder Regularity ⋮ Local Convergence of the FEM for the Integral Fractional Laplacian ⋮ Efficient Monte Carlo Method for Integral Fractional Laplacian in Multiple Dimensions ⋮ Analysis of a sinc-Galerkin Method for the Fractional Laplacian ⋮ Discretised general fractional derivative ⋮ Robust BPX preconditioner for fractional Laplacians on bounded Lipschitz domains ⋮ Finite element approximation of optimal control problem with integral fractional Laplacian and state constraint ⋮ Error estimates for fractional semilinear optimal control on Lipschitz polytopes ⋮ Adaptive finite element approximation of optimal control problems with the integral fractional Laplacian ⋮ Fractional elliptic problems on Lipschitz domains: regularity and approximation ⋮ An a posteriori error estimator for the spectral fractional power of the Laplacian ⋮ Constructive approximation on graded meshes for the integral fractional Laplacian ⋮ Optimal control of mixed local-nonlocal parabolic PDE with singular boundary-exterior data
Cites Work
- Unnamed Item
- Unnamed Item
- The second eigenvalue of the fractional \(p\)-Laplacian
- Local behavior of fractional \(p\)-minimizers
- Meyers inequality and strong stability for stable-like operators
- Fractional Laplacians on domains, a development of Hörmander's theory of \(\mu\)-transmission pseudodifferential operators
- Interior regularity of solutions of non-local equations in Sobolev and Nikol'skii spaces
- Local elliptic regularity for the Dirichlet fractional Laplacian
- A posteriori error analysis for a class of integral equations and variational inequalities
- Direct and inverse error estimates for finite elements with mesh refinements
- Regularity results for elliptic equations in Lipschitz domains
- A novel and accurate finite difference method for the fractional Laplacian and the fractional Poisson problem
- A short FE implementation for a 2d homogeneous Dirichlet problem of a fractional Laplacian
- Numerical approximation of the integral fractional Laplacian
- Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary element methods. II: The three-dimensional case
- Space-time adaptive finite elements for nonlocal parabolic variational inequalities
- Accurate numerical methods for two and three dimensional integral fractional Laplacian with applications
- Adaptive finite element method for fractional differential equations using hierarchical matrices
- Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver
- Nonlocal self-improving properties
- The Dirichlet problem for the fractional Laplacian: regularity up to the boundary
- Lower bounds of the discretization error for piecewise polynomials
- Analysis of the Scott–Zhang interpolation in the fractional order Sobolev spaces
- A Fractional Laplace Equation: Regularity of Solutions and Finite Element Approximations
- Local energy estimates for the finite element method on sharply varying grids
- First Passage Times for Symmetric Stable Processes in Space
- An adaptive finite element method for two-phase Stefan problems in two space dimensions. I. Stability and error estimates
- Interior Estimates for Ritz-Galerkin Methods
- Localization of the Aronszajn-Slobodeckij norm and application to adaptive boundary elements methods. Part I. The two-dimensional case
- Quasi-optimal convergence rate for an adaptive method for the integral fractional Laplacian
- Linear and nonlinear fractional elliptic problems
- On the Convergence in $H^1$-Norm for the Fractional Laplacian
- Numerical Methods for the Fractional Laplacian: A Finite Difference-Quadrature Approach
- EQUATIONS IN CONVOLUTIONS IN A BOUNDED REGION
- Numerical methods for fractional diffusion
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