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Electronic Research Archive

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, 29(4): 2755-2770 doi: 10.3934/era.2021012 +[Abstract](449)+[HTML](189) +[PDF](4771.42KB)
Abstract:

We present a posteriori error estimator strategies for the least-squares finite element method (LS) to approximate the exponential Phan-Thien-Tanner (PTT) viscoelastic fluid flows. The error estimator provides adaptive mass weights and mesh refinement criteria for improving LS solutions using lower-order basis functions and a small number of elements. We analyze an a priori error estimate for the first-order linearized LS system and show that the estimate is supported by numerical results. The LS approach is numerically tested for a convergence study and then applied to the flow past a slot channel. Numerical results verify that the proposed approach improves numerical solutions and resolves computational difficulties related to the presence of corner singularities and limitations arising from the exorbitant number of unknowns.

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:
A multigrid based finite difference method for solving parabolic interface problemSpecial Issues
Hongsong Feng and Shan Zhao
2021,  doi: 10.3934/era.2021031 +[Abstract](15)+[HTML](11) +[PDF](18671.43KB)
Abstract:
A conforming-nonconforming mixed immersed finite element method for unsteady Stokes equations with moving interfacesSpecial Issues
Derrick Jones and Xu Zhang
2021,  doi: 10.3934/era.2021032 +[Abstract](15)+[HTML](11) +[PDF](1840.69KB)
Abstract:
Immersed hybrid difference methods for elliptic boundary value problems by artificial interface conditionsSpecial Issues
Youngmok Jeon and Dongwook Shin
2021,  doi: 10.3934/era.2021043 +[Abstract](15)+[HTML](11) +[PDF](471.45KB)
Abstract:
Accelerating the Bayesian inference of inverse problems by using data-driven compressive sensing method based on proper orthogonal decompositionSpecial Issues
Meixin Xiong, Liuhong Chen, Ju Ming and Jaemin Shin
2021,  doi: 10.3934/era.2021044 +[Abstract](15)+[HTML](11) +[PDF](827.29KB)
Abstract:
An adjoint-based a posteriori analysis of numerical approximation of Richards equationSpecial Issues
Victor Ginting
2021,  doi: 10.3934/era.2021045 +[Abstract](15)+[HTML](11) +[PDF](453.31KB)
Abstract:
A stabilizer free WG method for the Stokes equations with order two superconvergence on polytopal meshSpecial Issues
Xiu Ye and Shangyou Zhang
2021,  doi: 10.3934/era.2021053 +[Abstract](15)+[HTML](11) +[PDF](5387.74KB)
Abstract:
A simple virtual element-based flux recovery on quadtreeSpecial Issues
Shuhao Cao
2021,  doi: 10.3934/era.2021054 +[Abstract](15)+[HTML](11) +[PDF](801.83KB)
Abstract:
Some estimates of virtual element methods for fourth order problemsSpecial Issues
Jiaxin Zhang, Hoang Tran and Guannan Zhang
2021,  doi: 10.3934/era.2021074 +[Abstract](15)+[HTML](11) +[PDF](2236.08KB)
Abstract:
Accelerating reinforcement learning with a Directional-Gaussian-Smoothing evolution strategySpecial Issues
Qingguang Guan
2021,  doi: 10.3934/era.2021075 +[Abstract](15)+[HTML](11) +[PDF](336.86KB)
Abstract:

2020 Impact Factor: 1.833
5 Year Impact Factor: 1.833

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