Preface to the Special Issue in Memory of Professor Saul Abarbanel Alina Chertock, Adi Ditkowski, Anne Gelb, Sigal Gottlieb, Saul Abarbanel 

Half a Century of Scientific Work
Bertil Gustafsson 

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

Smoothness-Increasing Accuracy-Conserving (SIAC) Filtering for Discontinuous Galerkin Solutions over Nonuniform Meshes: Superconvergence and Optimal Accuracy
Xiaozhou Li, Jennifer K. Ryan, Robert M. Kirby, K. Vuik

Compact High Order Accurate Schemes for the Three Dimensional Wave Equation

F. Smith, S. Tsynkov, E. Turkel

Certified Offline-Free Reduced Basis (COFRB) Methods for Stochastic Differential Equations Driven by Arbitrary Types of Noise
Yong Liu, Tianheng Chen, Yanlai Chen, Chi-Wang Shu  

Numerical Analysis for Conservation Laws Using  l1-Minimization
Anne Gelb, X. Hou, Q. Li  

A Source of Uncertainty in Computed Discontinuous Flows
Michael Sever  

One-Dimensional/Two-Dimensional Coupling Approach with Quadrilateral Confluence Region for Modeling River Systems
Xin Liu, Alina Chertock, Alexander Kurganov, K. Wolfkill 

Generalized Sensitivity Parameter Free Fifth Order WENO Finite Difference Scheme with Z-Type Weights
Yinghua Wang, Bao-Shan Wang, Wai Sun Don 

Entropy Stable Method for the Euler Equations Revisited: Central Differencing via Entropy Splitting and SBP
Bjorn Sjogreen, H. C. Yee 

A Cartesian Compact Scheme for the Navier–Stokes Equations in Streamfunction Formulation in Irregular Domains
Matania Ben-Artzi, Jean-Pierre Croisille, Dalia Fishelov 

Adaptive Time Steps for Compressible Flows Based on Dual-Time Stepping and a RK/Implicit Smoother
O. Peles, E. Turkel 

A Second Order Traffic Flow Model with Lane Changing
Jiah Song, Smadar Karni

Strong Stability Preserving Integrating Factor Two-Step Runge–Kutta Methods
Leah Isherwood, Zachary J. Grant, Sigal Gottlieb

Complementary Solutions of Nitsche’s Method
Isaac Harari, Uri Albocher 

An Accurate Approximation of Exponential Integrators for the Schrödinger Equation
A. Y. Meltzer 

Discontinuous Galerkin Difference Methods for Symmetric Hyperbolic Systems
T. Hagstrom, J. W. Banks, B. B. Buckner, K. Juhnke 

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, Mark Sussman, M. Yousuff Hussaini

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

Superconvergence Points for the Spectral Interpolation of Riesz Fractional Derivatives
Beichuan Deng, Zhimin Zhang, Xuan Zhao

Superconvergent Recovery of Rectangular Edge Finite Element Approximation by Local Symmetry Projection
Chao Wu, Yunqing Huang, Nianyu Yi, Jinyun Yuan

Diffusion Across Semi-permeable Barriers: Spectral Properties, Efficient Computation, and Applications
Nicolas Moutal, Denis Grebenkov 

Analysis of Spectral Approximations Using Eigenfunctions of Fractional Sturm–Liouville Problems
Haiyong Wang 

A Decoupled, Linear and Unconditionally Energy Stable Scheme with Finite Element Discretizations for Magneto-Hydrodynamic Equations
Guo-Dong Zhang, XiaoMing He, XiaoFeng Yang

Multiscale Hybridizable Discontinuous Galerkin Method for Flow Simulations in Highly Heterogeneous Media
Yanfang Yang, Ke Shi, Shubin Fu 

Discontinuity-Detecting Method for a Four-Point Stencil and Its Application to Develop a Third-Order Hybrid-WENO Scheme
Shengping Liu, Yiqing Shen

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

Error Bounds of the Finite Difference Time Domain Methods for the Dirac Equation in the Semiclassical Regime
Ying Ma, Jia Yin 

Nonconforming Virtual Element Method for the Time Fractional Reaction–Subdiffusion Equation with Non-smooth Data
Meng Li, Jikun Zhao, Chengming Huang, Shaochun Chen

An Efficient Boundary Integral Scheme for the Threshold Dynamics Method II: Applications to Wetting Dynamics
Dong Wang, Shidong Jiang, Xiao-Ping Wang

Superconvergent Recovery of Raviart–Thomas Mixed Finite Elements on Triangular Grids
Randolph E. Bank, Yuwen Li

Modified Ghost Fluid Method with Acceleration Correction (MGFM/AC)
Tiegang Liu, Chengliang Feng, Liang Xu

Explicit Time Stepping of PDEs with Local Refinement in Space-Time
Dylan Abrahamsen, Bengt Fornberg

High Order Anchoring and Reinitialization of Level Set Function for Simulating Interface Motion
Vimal Ramanuj, Ramanan Sankaran

Polynomial Chaos Level Points Method for One-Dimensional Uncertain Steep Problems
Pierre Sochala, Olivier Le Maître

Ordered Line Integral Methods for Solving the Eikonal Equation
Samuel F. Potter, Maria K. Cameron

Residual-Based a Posteriori Error Estimation for Immersed Finite Element Methods
Cuiyu He, Xu Zhang

Implicit–Explicit Local Discontinuous Galerkin Methods with Generalized Alternating Numerical Fluxes for Convection–Diffusion Problems
Haijin Wang, Qiang Zhang, Chi-Wang Shu 

Well-Balanced Discontinuous Galerkin Method for Shallow Water Equations with Constant Subtraction Techniques on Unstructured Meshes
Huijing Du, Yingjie Liu, Yuan Liu, Zhiliang Xu

Capturing Composite Waves in Non-convex Special Relativistic Hydrodynamics
Antonio Marquina, Susana Serna, José M. Ibáñez 

A Müntz-Collocation Spectral Method for Weakly Singular Volterra Integral Equations
Dianming Hou, Yumin Lin, Mejdi Azaiez, Chuanju Xu

Superconvergent Interpolatory HDG Methods for Reaction Diffusion Equations I: An HDGk Method
Gang Chen, Bernardo Cockburn, John Singler, Yangwen Zhang

Discrete Kernel Preserving Model for 3D Electron–Optical Phonon Scattering Under Arbitrary Band Structures
Wenqi Yao, Tiao Lu 

Energy Decay and Stability of a Perfectly Matched Layer For the Wave Equation
Daniel H. Baffet, Marcus J. Grote, Sébastien Imperiale, Maryna Kachanovska

A Finite Element/Operator-Splitting Method for the Numerical Solution of the Three Dimensional Monge–Ampère Equation
Hao Liu, Roland Glowinski, Shingyu Leung, Jianliang Qian

An h–p Version of the Discontinuous Galerkin Method for Volterra Integro-Differential Equations with Vanishing Delays
Lina Wang, Lijun Yi 

A Finite Element Nonoverlapping Domain Decomposition Method with Lagrange Multipliers for the Dual Total Variation Minimizations
Chang-Ock Lee, Jongho Park

Accuracy of Stable, High-order Finite Difference Methods for Hyperbolic Systems with Non-smooth Wave Speeds
Brittany A. Erickson, Ossian O’Reilly, Jan Nordström 

Virtual Element Method for an Elliptic Hemivariational Inequality with Applications to Contact Mechanics
Fang Feng, Weimin Han, Jianguo Huang

Asymptotic Stability of Compact and Linear \theta-Methods for Space Fractional Delay Generalized Diffusion Equation
Qifeng Zhang, Tingyue Li

Entropy and Adjoint Methods
Carlos Lozano

Improved Characteristic Fast Marching Method for the Generalized Eikonal Equation in a Moving Medium
Myong-Song Ho, Ju-Hyok Ri, Sin-Bom Kim