Raytcho Lazarov

Texas A&M University, Mathematics, Faculty Member

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MS, Wroclaw University, 1966
PhD, Moscow University, 1972
DrSci., Sofia University, 1982
Supervisors: A.A. Samarskii, PhD
Address: Department of Mathematics
Texas A&M University
College Station, TX 77843, USA

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Papers by Raytcho Lazarov

Numerical Approximation of Fractional Powers of Elliptic Operators

arXiv (Cornell University), Mar 27, 2018

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A note on the uniform inf-sup condition for the Brinkman problem in highly heterogeneous media

Journal of Computational and Applied Mathematics, Oct 1, 2018

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First-Order System Least Squares for Second-Order Partial Differential Equations: Part I

SIAM Journal on Numerical Analysis, Dec 1, 1994

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Superconvergence of mixed finite element methods for parabolic problems with nonsmooth initial data

Numerische Mathematik, Feb 1, 1998

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Integral Equations and Inverse Problems

... Integral equations and inverse problems. Author: Brahm Alexander Rhodes, Publication: · Docto... more

Разностные схемы для дифференциальных уравнений с обобщенными решениями

Functional a posteriori error estimates for discontinuous Galerkin approximations of elliptic problems

Numerical Methods for Partial Differential Equations, Jul 1, 2009

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$Research paper thumbnail of Numerical approximation of fractional powers of elliptic operators$

Numerical approximation of fractional powers of elliptic operators

Ima Journal of Numerical Analysis, Mar 28, 2019

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Error Estimates for a Finite Volume Element Method for Elliptic PDEs in Nonconvex Polygonal Domains

SIAM Journal on Numerical Analysis, 2005

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Error estimates for a finite volume element method for parabolic equations in convex polygonal domains

Numerical Methods for Partial Differential Equations, Mar 2, 2004

Optimal Solvers for Linear Systems with Fractional Powers of Sparse SPD Matrices

arXiv (Cornell University), Dec 14, 2016

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A Survey on Numerical Methods for Spectral Space-Fractional Diffusion Problems

arXiv (Cornell University), Oct 3, 2020

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An analysis of the L1 scheme for the subdiffusion scheme with nonsmooth data

The subdiffusion equation with a Caputo fractional derivative of order α∈(0,1) in time arises in ... more The subdiffusion equation with a Caputo fractional derivative of order α∈(0,1) in time arises in a wide variety of practical applications, and it is often adopted to model anomalous subdiffusion processes in heterogeneous media. The L1 scheme is one of the most popular and successful numerical methods for discretizing the Caputo fractional derivative in time. The scheme was analysed earlier independently by Lin and Xu (2007, Finite difference/spectral approximations for the time-fractional diffusion equation. J. Comput. Phys., 225, 1533–1552) and Sun and Wu (2006, A fully discrete scheme for a diffusion wave system. Appl. Numer. Math., 56, 193–209), and an O(τ2−α) convergence rate was established, under the assumption that the solution is twice continuously differentiable in time. However, in view of the smoothing property of the subdiffusion equation, this regularity condition is restrictive, since it does not hold even for the homogeneous problem with a smooth initial data. In this work, we revisit the error analysis of the scheme, and establish an O(τ) convergence rate for both smooth and nonsmooth initial data. The analysis is valid for more general sectorial operators. In particular, the L1 scheme is applied to one-dimensional space-time fractional diffusion equations, which involves also a Riemann–Liouville derivative of order β∈(32,2) in space, and error estimates are provided for the fully discrete scheme. Numerical experiments are provided to verify the sharpness of the error estimates, and robustness of the scheme with respect to data regularity.

$Research paper thumbnail of Variational formulation of problems involving fractional order differential operators$

Variational formulation of problems involving fractional order differential operators

arXiv (Cornell University), Jul 17, 2013

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A Numerical Study of the Homogeneous Elliptic Equation with Fractional Boundary Conditions

Fractional Calculus and Applied Analysis, Apr 1, 2017

We consider the homogeneous equation

$Research paper thumbnail of Error estimates for a semidiscrete finite element method for fractional order parabolic equations$

Error estimates for a semidiscrete finite element method for fractional order parabolic equations

arXiv (Cornell University), Apr 17, 2012

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Solving elliptic problems by the domain decomposition method using preconditioning matrices derived by multilevel splittings of the finite element matrix

Springer eBooks, 1988

... For this see Dryja, Proskurow-ski & Widlund [14], Dryja, Proskurowski []3], Bramble, Pasc... more ... For this see Dryja, Proskurow-ski & Widlund [14], Dryja, Proskurowski []3], Bramble, Pasciack, Schatz [61, [7], [8]. To complete the DD we have to ... k) is used (the so - called inverse - free version, for details see Axelsson & Polman 3 ). Let B be a block tridiagonal matrix (Bi,i_4, Bii ...