293 citations · 793 across the 29 of their papers we have counts for
30 papers
A Survey on Numerical Methods for Spectral Space-Fractional Diffusion Problems
Stanislav Harizanov, Raytcho Lazarov, Svetozar Margenov
The survey is devoted to numerical solution of the fractional equation , , where is a symmetric positive definite operator corresponding to a second order elli…
The Best Uniform Rational Approximation: Applications to Solving Equations Involving Fractional powers of Elliptic Operators
Stanislav Harizanov, Raytcho Lazarov, Svetozar Margenov +1
In this paper we consider one particular mathematical problem of this large area of fractional powers of self-adjoined elliptic operators, defined either by Dunford-Taylor-like int…
Analysis of numerical methods for spectral fractional elliptic equations based on the best uniform rational approximation
Stanislav Harizanov, Raytcho Lazarov, Pencho Marinov +2
Here we study theoretically and compare experimentally an efficient method for solving systems of algebraic equations, where the matrix comes from the discretization of a fractiona…
Numerical methods for time-fractional evolution equations with nonsmooth data: a concise overview
Bangti Jin, Raytcho Lazarov, Zhi Zhou
Over the past few decades, there has been substantial interest in evolution equations that involving a fractional-order derivative of order in time, due to their many s…
Comparison analysis on two numerical methods for fractional diffusion problems based on rational approximations of
Stanislav Harizanov, Raytcho Lazarov, Pencho Marinov +2
We discuss, study, and compare experimentally three methods for solving the system of algebraic equations , , where is a symmetric a…
Numerical Approximation of Fractional Powers of Elliptic Operators
Beiping Duan, Raytcho Lazarov, Joeseph Pasciak
In this paper, we develop and study algorithms for approximately solving the linear algebraic systems: , , for with a fi…
Space-Time Petrov-Galerkin FEM for Fractional Diffusion Problems
Beiping Duan, Bangti Jin, Raytcho Lazarov +2
We present and analyze a space-time Petrov-Galerkin finite element method for a time-fractional diffusion equation involving a Riemann-Liouville fractional derivative of order $α\i…
A numerical study of the homogeneous elliptic equation with fractional order boundary conditions
Raytcho Lazarov, Petr Vabishchevich
We consider the homogeneous equation , where is a symmetric and coercive elliptic operator in with bounded domain in .…
Optimal Solvers for Linear Systems with Fractional Powers of Sparse SPD Matrices
Stanislav Harizanov, Raytcho Lazarov, Pencho Marinov +2
In this paper we consider efficient algorithms for solving the algebraic equation , , where is a symmetric and positive defini…
Geometric Multigrid for Darcy and Brinkman models of flows in highly heterogeneous porous media: A numerical study
Guido Kanschat, Raytcho Lazarov, Youli Mao
We apply geometric multigrid methods for the finite element approximation of flow problems governed by Darcy and Brinkman systems used in modeling highly heterogeneous porous media…
A Petrov-Galerkin Finite Element Method for Fractional Convection-Diffusion Equations
Bangti Jin, Raytcho Lazarov, Zhi Zhou
In this work, we develop variational formulations of Petrov-Galerkin type for one-dimensional fractional boundary value problems involving either a Riemann-Liouville or Caputo deri…
On Nonnegativity Preservation in Finite Element Methods for Subdiffusion Equations
Bangti Jin, Raytcho Lazarov, Vidar Thomée +1
We consider three types of subdiffusion models, namely single-term, multi-term and distributed order fractional diffusion equations, for which the maximum-principle holds and which…
Error Estimates for Approximations of Distributed Order Time Fractional Diffusion with Nonsmooth Data
Bangti Jin, Raytcho Lazarov, Dongwoo Sheen +1
In this work, we consider the numerical solution of an initial boundary value problem for the distributed order time fractional diffusion equation. The model arises in the mathemat…
A simple finite element method for the boundary value problem with a Riemann-Liouville derivative
Bangti Jin, Raytcho Lazarov, Xiliang Lu +1
We consider a boundary value problem involving a Riemann-Liouville fractional derivative of order on the unit interval . The standard Galerkin finite element…
An analysis of the L1 Scheme for the subdiffusion equation with nonsmooth data
Bangti Jin, Raytcho Lazarov, Zhi Zhou
The subdiffusion equation with a Caputo fractional derivative of order in time arises in a wide variety of practical applications, and it is often adopted to model anom…
Preconditioning of weighted H(div)-norm and applications to numerical simulation of highly heterogeneous media
Johannes Kraus, Raytcho Lazarov, Maria Lymbery +2
In this paper we propose and analyze a preconditioner for a system arising from a finite element approximation of second order elliptic problems describing processes in highly het-…
Two Schemes for Fractional Diffusion and Diffusion-Wave Equations with Nonsmooth Data
Bangti Jin, Raytcho Lazarov, Zhi Zhou
We consider the initial/boundary value problem for the fractional diffusion and diffusion-wave equations involving a Caputo fractional derivative in time. We develop two "simple" f…
An Analysis of the Rayleigh-Stokes problem for a Generalized Second-Grade Fluid
Emilia Bazhlekova, Bangti Jin, Raytcho Lazarov +1
We study the Rayleigh-Stokes problem for a generalized second-grade fluid which involves a Riemann-Liouville fractional derivative in time, and present an analysis of the problem i…
The Galerkin Finite Element Method for A Multi-term Time-Fractional Diffusion equation
Bangti Jin, Raytcho Lazarov, Yikan Liu +1
We consider the initial/boundary value problem for a diffusion equation involving multiple time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space sem…
A multiscale HDG method for second order elliptic equations. Part I. Polynomial and homogenization-based multiscale spaces
Yalchin Efendiev, Raytcho Lazarov, Ke Shi
We introduce a finite element method for numerical upscaling of second order elliptic equations with highly heterogeneous coefficients. The method is based on a mixed formulation o…
Error Analysis of Finite Element Methods for Space-Fractional Parabolic Equations
Bangti Jin, Raytcho Lazarov, Joseph Pasciak +1
We consider an initial/boundary value problem for one-dimensional fractional-order parabolic equations with a space fractional derivative of Riemann-Liouville type and order $α\in…
A Finite Element Method for the Fractional Sturm-Liouville Problem
Bangti Jin, Raytcho Lazarov, Joseph Pasciak +1
In this work, we propose an efficient finite element method for solving fractional Sturm-Liouville problems involving either the Caputo or Riemann-Liouville derivative of order $α\…
Variational formulation of problems involving fractional order differential operators
Bangti Jin, Raytcho Lazarov, Joseph Pasciak
In this work, we consider boundary value problems involving Caputo and Riemann-Liouville fractional derivatives of order on the unit interval . These fractional…
Error Analysis of Semidiscrete Finite Element Methods for Inhomogeneous Time-Fractional Diffusion
Bangti Jin, Raytcho Lazarov, Joseph Pasciak +1
We consider the initial boundary value problem for the inhomogeneous time-fractional diffusion equation with a homogeneous Dirichlet boundary condition and a nonsmooth right hand s…