A reduced basis method for fractional diffusion operators. II
DOI10.1515/jnma-2020-0042zbMath1491.65131arXiv2005.03574OpenAlexW3135437804MaRDI QIDQ2070268
Tobias Danczul, Joachim Schöberl
Publication date: 24 January 2022
Published in: Journal of Numerical Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2005.03574
Error bounds for boundary value problems involving PDEs (65N15) Fractional derivatives and integrals (26A33) Completeness of eigenfunctions and eigenfunction expansions in context of PDEs (35P10) 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) Second-order elliptic equations (35J15) Interpolation between normed linear spaces (46B70) Numerical methods for eigenvalue problems for boundary value problems involving PDEs (65N25) Fractional partial differential equations (35R11)
Related Items (6)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Ten equivalent definitions of the fractional Laplace operator
- The periodic patch model for population dynamics with fractional diffusion
- Numerically solving an equation for fractional powers of elliptic operators
- An introduction to Sobolev spaces and interpolation spaces
- \(\mathcal {H}\)-matrix approximability of the inverses of FEM matrices
- Reduced basis approximation and a posteriori error estimation for affinely parametrized elliptic coercive partial differential equations. Application to transport and continuum mechanics.
- Positive solutions of nonlinear problems involving the square root of the Laplacian
- NETGEN: An advancing front 2D/3D-mesh generator based on abstract rules
- Global a priori convergence theory for reduced-basis approximations of single-parameter symmetric coercive elliptic partial differential equations
- Analysis of numerical methods for spectral fractional elliptic equations based on the best uniform rational approximation
- A unified view of some numerical methods for fractional diffusion
- What is the fractional Laplacian? A comparative review with new results
- Spectral approximation of fractional PDEs in image processing and phase field modeling
- \({\mathscr{H}} \)-matrix approximability of inverses of discretizations of the fractional Laplacian
- Aspects of an adaptive finite element method for the fractional Laplacian: a priori and a posteriori error estimates, efficient implementation and multigrid solver
- On sinc quadrature approximations of fractional powers of regularly accretive operators
- Tensor FEM for spectral fractional diffusion
- A PDE approach to fractional diffusion in general domains: a priori error analysis
- A concave—convex elliptic problem involving the fractional Laplacian
- A New Type of Identification Problems: Optimizing the Fractional Order in a Nonlocal Evolution Equation
- Extension Problem and Harnack's Inequality for Some Fractional Operators
- Regularity of Radial Extremal Solutions for Some Non-Local Semilinear Equations
- Nonlocal Operators with Applications to Image Processing
- Optimal solvers for linear systems with fractional powers of sparse SPD matrices
- $hp$-Finite Elements for Fractional Diffusion
- Hybrid Finite Element--Spectral Method for the Fractional Laplacian: Approximation Theory and Efficient Solver
- Towards an Efficient Finite Element Method for the Integral Fractional Laplacian on Polygonal Domains
- hp-FEM for the fractional heat equation
- Sobolev Spaces with Non-Muckenhoupt Weights, Fractional Elliptic Operators, and Applications
- Reduced Basis Methods for Fractional Laplace Equations via Extension
- Numerical approximation of fractional powers of elliptic operators
- An Extension Problem Related to the Fractional Laplacian
- Reduced Basis Methods for Partial Differential Equations
- ZOLOTAREV PROBLEMS CONNECTED WITH RATIONAL FUNCTIONS
- Multilevel methods for nonuniformly elliptic operators and fractional diffusion
- Galerkin proper orthogonal decomposition methods for parabolic problems
- Numerical methods for fractional diffusion
This page was built for publication: A reduced basis method for fractional diffusion operators. II