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Special issue on recent advances in numerical analysis

Mahboub Baccouch, Department of Mathematics, University of Nebraska at Omaha, 6001 Dodge Street, Omaha, NE 68182-0243 USA mbaccouch@unomaha.edu
Xiaoming He, Department of Mathematics and Statistics, Missouri University of Science and Technology, 400 W. 12th St., Rolla, MO 65401 USA hex@mst.edu
Daozhi Han, Department of Mathematics and Statistics, Missouri University of Science and Technology, 400 W. 12th St., Rolla, MO 65401 USA handaoz@mst.edu
Nan Jiang, Department of Mathematics, Little Hall 358, University of Florida, 1400 Stadium Rd, Gainesville, FL 32611 USA jiangn@mst.edu
Fritz Keinert, Department of Mathematics, 464 Carver Hall, Iowa State University, 411 Morrill Road, Ames, IA 50011 USA keinert@iastate.edu

An a posteriori error estimator based on least-squares finite element solutions for viscoelastic fluid flowsSpecial Issues
Hsueh-Chen Lee   and Hyesuk Lee
2021,  doi: 10.3934/era.2021012 +[Abstract](15)+[HTML](11) +[PDF](4744.99KB)
Abstract:

In this paper, we consider a kind of efficient finite difference methods (FDMs) for solving the nonlinear Helmholtz equation in the Kerr medium. Firstly, by applying several iteration methods, we linearize the nonlinear Helmholtz equation in several different ways. Then, based on the resulted linearized problem at each iterative step, by rearranging the Taylor expansion and using the ADI method, we deduce a kind of new FDMs, which also provide a route to deal with the problem with discontinuous coefficients.Finally, some numerical results are presented to validate the efficiency of the proposed schemes, and to show that our schemes perform with much higher accuracy and better convergence compared with the classical ones.

Convergence analysis of Fourier pseudo-spectral schemes for three-dimensional incompressible Navier-Stokes equationsSpecial Issues
Cheng Wang
2020,  doi: 10.3934/era.2021019 +[Abstract](15)+[HTML](11) +[PDF](495.86KB)
Abstract:

Title change has delayed IF

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