1. Preface to the Special Issue in Memory of Professor Saul Abarbanel

   • Alina Chertock
   • Adi Ditkowski
   • Semyon Tsynkov

   Editorial 11 November 2019 Pages: 1119 - 1123

   

2. Saul Abarbanel; Half a Century of Scientific Work

   • Bertil Gustafsson

   Review paper Open access 28 March 2019 Pages: 1124 - 1135

   

3. An Iteration-Free Approach to Solving the Navier–Stokes Equations by Implicit Finite Difference Schemes in the Vorticity-Stream Function Formulation

   • V. S. Ryaben’kii
   • V. A. Torgashov

   OriginalPaper 11 March 2019 Pages: 1136 - 1149

   

4. Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Discontinuous Galerkin Solutions over Nonuniform Meshes: Superconvergence and Optimal Accuracy

   • Xiaozhou Li
   • Jennifer K. Ryan
   • Kees Vuik

   OriginalPaper Open access 13 February 2019 Pages: 1150 - 1180

   

5. Compact High Order Accurate Schemes for the Three Dimensional Wave Equation

   • F. Smith
   • S. Tsynkov
   • E. Turkel

   OriginalPaper 06 May 2019 Pages: 1181 - 1209

   

6. Certified Offline-Free Reduced Basis (COFRB) Methods for Stochastic Differential Equations Driven by Arbitrary Types of Noise

   • Yong Liu
   • Tianheng Chen
   • Chi-Wang Shu

   OriginalPaper 16 May 2019 Pages: 1210 - 1239

   

7. Numerical Analysis for Conservation Laws Using \(l_1\) Minimization

   • Anne Gelb
   • X. Hou
   • Q. Li

   OriginalPaper 03 June 2019 Pages: 1240 - 1265

   

8. A Source of Uncertainty in Computed Discontinuous Flows

   • Michael Sever

   OriginalPaper 02 July 2019 Pages: 1266 - 1296

9. One-Dimensional/Two-Dimensional Coupling Approach with Quadrilateral Confluence Region for Modeling River Systems

   • Xin Liu
   • Alina Chertock
   • Karlan Wolfkill

   OriginalPaper 27 June 2019 Pages: 1297 - 1328

   

10. Generalized Sensitivity Parameter Free Fifth Order WENO Finite Difference Scheme with Z-Type Weights

    • Yinghua Wang
    • Bao-Shan Wang
    • Wai Sun Don

    OriginalPaper 03 July 2019 Pages: 1329 - 1358

    

11. Entropy Stable Method for the Euler Equations Revisited: Central Differencing via Entropy Splitting and SBP

    • Björn Sjögreen
    • H. C. Yee

    OriginalPaper 29 July 2019 Pages: 1359 - 1385

    

12. A Cartesian Compact Scheme for the Navier–Stokes Equations in Streamfunction Formulation in Irregular Domains

    • Matania Ben-Artzi
    • Jean-Pierre Croisille
    • Dalia Fishelov

    OriginalPaper 16 July 2019 Pages: 1386 - 1408

    

13. Adaptive Time Steps for Compressible Flows Based on Dual-Time Stepping and a RK/Implicit Smoother

    • O. Peles
    • E. Turkel

    OriginalPaper 07 August 2019 Pages: 1409 - 1428

    

14. A Second Order Traffic Flow Model with Lane Changing

    • Jiah Song
    • Smadar Karni

    OriginalPaper 02 August 2019 Pages: 1429 - 1445

    

15. Strong Stability Preserving Integrating Factor Two-Step Runge–Kutta Methods

    • Leah Isherwood
    • Zachary J. Grant
    • Sigal Gottlieb

    OriginalPaper 13 September 2019 Pages: 1446 - 1471

    

16. Complementary Solutions of Nitsche’s Method

    • Isaac Harari
    • Uri Albocher

    OriginalPaper 17 October 2019 Pages: 1472 - 1492

    

17. An Accurate Approximation of Exponential Integrators for the Schrödinger Equation

    • A. Y. Meltzer

    OriginalPaper 04 November 2019 Pages: 1493 - 1508

    

18. Discontinuous Galerkin Difference Methods for Symmetric Hyperbolic Systems

    • T. Hagstrom
    • J. W. Banks
    • K. Juhnke

    OriginalPaper 19 October 2019 Pages: 1509 - 1526

    

19. A Hierarchical Space-Time Spectral Element and Moment-of-Fluid Method for Improved Capturing of Vortical Structures in Incompressible Multi-phase/Multi-material Flows

    • Chaoxu Pei
    • Mehdi Vahab
    • M. Yousuff Hussaini

    OriginalPaper 09 November 2019 Pages: 1527 - 1566

    

20. Comparing Gradient Descent with Automatic Differentiation and Particle Swarm Optimization Techniques for Estimating Tumor Blood Flow Parameters in Contrast-Enhanced Imaging

    • Kao-Pu Chang
    • Jessica M. Libertini
    • Steven Seay

    OriginalPaper 19 November 2019 Pages: 1567 - 1576

21. Superconvergence Points for the Spectral Interpolation of Riesz Fractional Derivatives

    • Beichuan Deng
    • Zhimin Zhang
    • Xuan Zhao

    OriginalPaper 26 September 2019 Pages: 1577 - 1601

    

22. Superconvergent Recovery of Rectangular Edge Finite Element Approximation by Local Symmetry Projection

    • Chao Wu
    • Yunqing Huang
    • Jinyun Yuan

    OriginalPaper 01 October 2019 Pages: 1602 - 1629

    

23. Diffusion Across Semi-permeable Barriers: Spectral Properties, Efficient Computation, and Applications

    • Nicolas Moutal
    • Denis Grebenkov

    OriginalPaper 26 September 2019 Pages: 1630 - 1654

    

24. Analysis of Spectral Approximations Using Eigenfunctions of Fractional Sturm–Liouville Problems

    • Haiyong Wang

    OriginalPaper 23 September 2019 Pages: 1655 - 1677

    

25. A Decoupled, Linear and Unconditionally Energy Stable Scheme with Finite Element Discretizations for Magneto-Hydrodynamic Equations

    • Guo-Dong Zhang
    • XiaoMing He
    • XiaoFeng Yang

    OriginalPaper 09 October 2019 Pages: 1678 - 1711

    

26. Multiscale Hybridizable Discontinuous Galerkin Method for Flow Simulations in Highly Heterogeneous Media

    • Yanfang Yang
    • Ke Shi
    • Shubin Fu

    OriginalPaper 03 October 2019 Pages: 1712 - 1731

    

27. Discontinuity-Detecting Method for a Four-Point Stencil and Its Application to Develop a Third-Order Hybrid-WENO Scheme

    • Shengping Liu
    • Yiqing Shen

    OriginalPaper 03 October 2019 Pages: 1732 - 1766

    

28. Numerical Schemes for Solving the Time-Fractional Dual-Phase-Lagging Heat Conduction Model in a Double-Layered Nanoscale Thin Film

    • Cui-cui Ji
    • Weizhong Dai
    • Zhi-zhong Sun

    OriginalPaper 09 October 2019 Pages: 1767 - 1800

    

29. Error Bounds of the Finite Difference Time Domain Methods for the Dirac Equation in the Semiclassical Regime

    • Ying Ma
    • Jia Yin

    OriginalPaper 08 October 2019 Pages: 1801 - 1822

30. Nonconforming Virtual Element Method for the Time Fractional Reaction–Subdiffusion Equation with Non-smooth Data

    • Meng Li
    • Jikun Zhao
    • Shaochun Chen

    OriginalPaper 09 October 2019 Pages: 1823 - 1859

    

31. An Efficient Boundary Integral Scheme for the Threshold Dynamics Method II: Applications to Wetting Dynamics

    • Dong Wang
    • Shidong Jiang
    • Xiao-Ping Wang

    OriginalPaper 19 October 2019 Pages: 1860 - 1881

    

32. Superconvergent Recovery of Raviart–Thomas Mixed Finite Elements on Triangular Grids

    • Randolph E. Bank
    • Yuwen Li

    OriginalPaper 18 October 2019 Pages: 1882 - 1905

    

33. Modified Ghost Fluid Method with Acceleration Correction (MGFM/AC)

    • Tiegang Liu
    • Chengliang Feng
    • Liang Xu

    OriginalPaper 01 November 2019 Pages: 1906 - 1944

    

34. Explicit Time Stepping of PDEs with Local Refinement in Space-Time

    • Dylan Abrahamsen
    • Bengt Fornberg

    OriginalPaper 16 October 2019 Pages: 1945 - 1962

    

35. High Order Anchoring and Reinitialization of Level Set Function for Simulating Interface Motion

    • Vimal Ramanuj
    • Ramanan Sankaran

    OriginalPaper 02 November 2019 Pages: 1963 - 1986

    

36. Polynomial Chaos Level Points Method for One-Dimensional Uncertain Steep Problems

    • Pierre Sochala
    • Olivier Le Maître

    OriginalPaper 22 October 2019 Pages: 1987 - 2009

    

37. Ordered Line Integral Methods for Solving the Eikonal Equation

    • Samuel F. Potter
    • Maria K. Cameron

    OriginalPaper 01 November 2019 Pages: 2010 - 2050

    

38. Residual-Based a Posteriori Error Estimation for Immersed Finite Element Methods

    • Cuiyu He
    • Xu Zhang

    OriginalPaper Open access 02 November 2019 Pages: 2051 - 2079

    

39. Implicit–Explicit Local Discontinuous Galerkin Methods with Generalized Alternating Numerical Fluxes for Convection–Diffusion Problems

    • Haijin Wang
    • Qiang Zhang
    • Chi-Wang Shu

    OriginalPaper 24 October 2019 Pages: 2080 - 2114

40. Well-Balanced Discontinuous Galerkin Method for Shallow Water Equations with Constant Subtraction Techniques on Unstructured Meshes

    • Huijing Du
    • Yingjie Liu
    • Zhiliang Xu

    OriginalPaper 02 November 2019 Pages: 2115 - 2131

    

41. Capturing Composite Waves in Non-convex Special Relativistic Hydrodynamics

    • Antonio Marquina
    • Susana Serna
    • José M. Ibáñez

    OriginalPaper 30 October 2019 Pages: 2132 - 2161

    

42. A Müntz-Collocation Spectral Method for Weakly Singular Volterra Integral Equations

    • Dianming Hou
    • Yumin Lin
    • Chuanju Xu

    OriginalPaper 30 October 2019 Pages: 2162 - 2187

    

43. Superconvergent Interpolatory HDG Methods for Reaction Diffusion Equations I: An HDG\(_{k}\) Method

    • Gang Chen
    • Bernardo Cockburn
    • Yangwen Zhang

    OriginalPaper 01 November 2019 Pages: 2188 - 2212

    

44. Discrete Kernel Preserving Model for 3D Electron–Optical Phonon Scattering Under Arbitrary Band Structures

    • Wenqi Yao
    • Tiao Lu

    OriginalPaper 09 November 2019 Pages: 2213 - 2236

    

45. Energy Decay and Stability of a Perfectly Matched Layer For the Wave Equation

    • Daniel H. Baffet
    • Marcus J. Grote
    • Maryna Kachanovska

    OriginalPaper 09 November 2019 Pages: 2237 - 2270

    

46. A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge–Ampère Equation

    • Hao Liu
    • Roland Glowinski
    • Jianliang Qian

    OriginalPaper 04 November 2019 Pages: 2271 - 2302

    

47. An h–p Version of the Discontinuous Galerkin Method for Volterra Integro-Differential Equations with Vanishing Delays

    • Lina Wang
    • Lijun Yi

    OriginalPaper 05 November 2019 Pages: 2303 - 2330

    

48. A Finite Element Nonoverlapping Domain Decomposition Method with Lagrange Multipliers for the Dual Total Variation Minimizations

    • Chang-Ock Lee
    • Jongho Park

    OriginalPaper 04 November 2019 Pages: 2331 - 2355

    

49. Accuracy of Stable, High-order Finite Difference Methods for Hyperbolic Systems with Non-smooth Wave Speeds

    • Brittany A. Erickson
    • Ossian O’Reilly
    • Jan Nordström

    OriginalPaper 11 November 2019 Pages: 2356 - 2387

    

50. Virtual Element Method for an Elliptic Hemivariational Inequality with Applications to Contact Mechanics

    • Fang Feng
    • Weimin Han
    • Jianguo Huang

    OriginalPaper 14 November 2019 Pages: 2388 - 2412