Latest Research in Advanced Numerical Methods in Computational Mathematics

35 research papers · 2026 median publication year

Top Research Topics in Advanced Numerical Methods in Computational Mathematics

Highest-Cited Papers

  1. A Hybrid High-Order Method for the Elasticity Problem with Linear Slip Interface
  2. Analysis of Compact Symmetric Finite Difference Methods with Highest Possible Orders for Elliptic Equations
  3. On $hp$-adaptive Structure-Preservation for the Cahn--Hilliard--Navier--Stokes Equations with Degenerate Mobility
  4. An efficient and rigorous criterion for the admissible time step of deforming grids in generalized Lagrangian and ALE methods
  5. A ϕ-FEM approach for time-dependent domains with unfitted meshes
  6. $hp$-a posteriori error estimates for hybrid high-order methods applied to biharmonic problems
  7. Guaranteed inf-sup bounds and existence verification for semilinear elliptic problems via nonconforming finite elements
  8. Tensor-Train Formulation and Numerical Study of the Peaceman–Rachford and Douglas–Rachford Splitting Schemes for Multidimensional Parabolic Evolution Equations
  9. SPECTRAL–COVARIANCE CLOSURE AND AUGMENTED RIGHT-INVERTIBILITY IN THE FORCED NAVIER–STOKES BLOWUP CONSTRUCTION: A STRUCTURAL RECONSTRUCTION
  10. Dirichlet-Neumann Waveform Relaxation Method for Hyperbolic PDE with Time Delay in Multiple Subdomains
  11. Mixed Hybrid High-Order Methods for Sixth-Order Problems: Fully Non-conforming and $C^0$-Conforming Discretizations
  12. Polynomial preserving recoveries of edge element method on Cartesian grids for the time-harmonic Maxwell equations with large wave number
  13. A Fully Discrete Local Discontinuous Galerkin Method for Quasilinear Stochastic Convection-Diffusion-Type Equations
  14. Boundary-Level-Constrained Refinement for Suppressing Trimming-Induced High-Frequency Outliers in Explicit Isogeometric Analysis
  15. High-Order Discontinuous Cut Finite Element Methods for Scalar Hyperbolic Conservation Laws
  16. Composite Wavelet Matrix-Based Transforms and Applications
  17. Invariant-region-preserving high-order schemes for a model of reactive sedimentation
  18. Robust High-Order Projector-Splitting Integrators
  19. A class of high-order discontinuous-Galerkin methods satisfying infinitely many entropy conditions with provable error estimates and strong convergence for general nonlinear conservation laws
  20. Scaling laws and energy dissipation in the dynamics of SLE curve as a 1D turbulence model
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L3 Region - - 2026 Sep Q3

Advanced Numerical Methods in Computational Mathematics

35 papers

Top Topics (9)

Numerical Analysis24
Advanced Numerical Methods in Computational Mathematics4
Tensor decomposition and applications1
Computation1
Statistical Mechanics1
Graphics1
Aerosol Filtration and Electrostatic Precipitation1
Probability1
Analysis of PDEs1

Top Publications (20)

1.A Hybrid High-Order Method for the Elasticity Problem with Linear Slip Interface2.Analysis of Compact Symmetric Finite Difference Methods with Highest Possible Orders for Elliptic Equations3.On $hp$-adaptive Structure-Preservation for the Cahn--Hilliard--Navier--Stokes Equations with Degenerate Mobility4.An efficient and rigorous criterion for the admissible time step of deforming grids in generalized Lagrangian and ALE methods5.A ϕ-FEM approach for time-dependent domains with unfitted meshes6.$hp$-a posteriori error estimates for hybrid high-order methods applied to biharmonic problems7.Guaranteed inf-sup bounds and existence verification for semilinear elliptic problems via nonconforming finite elements8.Tensor-Train Formulation and Numerical Study of the Peaceman–Rachford and Douglas–Rachford Splitting Schemes for Multidimensional Parabolic Evolution Equations9.SPECTRAL–COVARIANCE CLOSURE AND AUGMENTED RIGHT-INVERTIBILITY IN THE FORCED NAVIER–STOKES BLOWUP CONSTRUCTION: A STRUCTURAL RECONSTRUCTION10.Dirichlet-Neumann Waveform Relaxation Method for Hyperbolic PDE with Time Delay in Multiple Subdomains11.Mixed Hybrid High-Order Methods for Sixth-Order Problems: Fully Non-conforming and $C^0$-Conforming Discretizations12.Polynomial preserving recoveries of edge element method on Cartesian grids for the time-harmonic Maxwell equations with large wave number13.A Fully Discrete Local Discontinuous Galerkin Method for Quasilinear Stochastic Convection-Diffusion-Type Equations14.Boundary-Level-Constrained Refinement for Suppressing Trimming-Induced High-Frequency Outliers in Explicit Isogeometric Analysis15.High-Order Discontinuous Cut Finite Element Methods for Scalar Hyperbolic Conservation Laws16.Composite Wavelet Matrix-Based Transforms and Applications17.Invariant-region-preserving high-order schemes for a model of reactive sedimentation18.Robust High-Order Projector-Splitting Integrators19.A class of high-order discontinuous-Galerkin methods satisfying infinitely many entropy conditions with provable error estimates and strong convergence for general nonlinear conservation laws20.Scaling laws and energy dissipation in the dynamics of SLE curve as a 1D turbulence model
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