Abstract. We study PDE solution techniques for problems involving fractional powers of symmetric coercive elliptic operators in a bounded domain with Dirichlet boundary conditions. These operators can be realized as the Dirichlet to Neumann map of a degenerate/singular el-liptic problem posed on a semi-infinite cylinder, which we analyze in the framework of weighted Sobolev spaces. Motivated by the rapid decay of the solution of this problem, we propose a truncation that is suitable for numerical approximation. We discretize this truncation using first order tensor product finite elements. We derive a priori error estimates in weighted Sobolev spaces, which exhibit optimal regularity but suboptimal order for quasi-uniform meshes and quasi-o...
In this paper we develop and investigate numerical algorithms for solving equations of the first ord...
In this paper we study existence, regularity, and approximation of solution to a fractional semiline...
Low-rank tensor methods for the approximate solution of second-order elliptic partial diff...
Abstract. The purpose of this work is the study of solution techniques for problems involv-ing fract...
Abstract. The purpose of this work is the study of solution techniques for problems involv-ing fract...
Abstract. We study solution techniques for a linear-quadratic optimal control problem involving frac...
We propose and analyze a new discretization technique for a linear-quadratic optimal control problem...
Work completed. Exploiting the cylindrical extension proposed and investigated by X. Cabré and J. Ta...
Abstract. We study solution techniques for evolution equations with fractional diffusion and fractio...
We consider the homogeneous equation Au = 0, where A is a symmetric and coercive elliptic operator i...
We analyze the approximation by mixed finite element methods of solutions of equations of the form −...
Abstract. We derive a computable a posteriori error estimator for the α-harmonic extension problem, ...
The fractional Laplacian operator (−∆)s on a bounded domain Ω can be realized as a Dirichlet-to-Neum...
In this article we develop a posteriori error estimates for second order linear elliptic p...
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order...
In this paper we develop and investigate numerical algorithms for solving equations of the first ord...
In this paper we study existence, regularity, and approximation of solution to a fractional semiline...
Low-rank tensor methods for the approximate solution of second-order elliptic partial diff...
Abstract. The purpose of this work is the study of solution techniques for problems involv-ing fract...
Abstract. The purpose of this work is the study of solution techniques for problems involv-ing fract...
Abstract. We study solution techniques for a linear-quadratic optimal control problem involving frac...
We propose and analyze a new discretization technique for a linear-quadratic optimal control problem...
Work completed. Exploiting the cylindrical extension proposed and investigated by X. Cabré and J. Ta...
Abstract. We study solution techniques for evolution equations with fractional diffusion and fractio...
We consider the homogeneous equation Au = 0, where A is a symmetric and coercive elliptic operator i...
We analyze the approximation by mixed finite element methods of solutions of equations of the form −...
Abstract. We derive a computable a posteriori error estimator for the α-harmonic extension problem, ...
The fractional Laplacian operator (−∆)s on a bounded domain Ω can be realized as a Dirichlet-to-Neum...
In this article we develop a posteriori error estimates for second order linear elliptic p...
An unsteady problem is considered for a space-fractional equation in a bounded domain. A first-order...
In this paper we develop and investigate numerical algorithms for solving equations of the first ord...
In this paper we study existence, regularity, and approximation of solution to a fractional semiline...
Low-rank tensor methods for the approximate solution of second-order elliptic partial diff...