The field of numerical methods for complex systems is rapidly advancing, with a focus on developing innovative techniques for solving nonlinear problems, optimizing performance, and improving accuracy. Recent developments include the introduction of new finite element methods, such as the hybridizable discontinuous Galerkin method and the virtual element method, which offer improved stability and accuracy for a wide range of applications. Additionally, researchers are exploring the use of machine learning and artificial intelligence to improve the performance of numerical methods and reduce computational costs. Noteworthy papers include the development of a thermodynamically consistent phase-field model for mass transport with interfacial reaction and deformation, and the introduction of a high-order multigrid-preconditioned immersed interface solver for the Poisson equation with boundary and interface conditions. These advances have the potential to significantly impact fields such as fluid dynamics, materials science, and biomedicine, and will likely continue to drive innovation in the coming years.
Advances in Numerical Methods for Complex Systems
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A thermodynamically consistent phase-field model for mass transport with interfacial reaction and deformation
Numerical simulation of wormhole propagation with the mixed hybridized discontinuous Galerkin finite element method
A fourth-order cut-cell method for solving the two-dimensional advection-diffusion equation with moving boundaries
Numerical Simulations of Fully Eulerian Fluid-Structure Contact Interaction using a Ghost-Penalty Cut Finite Element Approach
A Comprehensive Framework for Predictive Computational Modeling of Growth and Remodeling in Tissue-Engineered Cardiovascular Implants
Babu\v{s}ka's paradox in a nonlinear bending model
High Accuracy Techniques Based Adaptive Finite Element Methods for Elliptic PDEs
Hardware Acceleration for HPS Algorithms in Two and Three Dimensions
A Spherical Crank-Nicolson Integrator Based on the Exponential Map and the Spherical Linear Interpolation
Accurate Error Estimates and Optimal Parameter Selection in Ewald Summation for Dielectrically Confined Coulomb Systems
Error analysis for temporal second-order finite element approximations of axisymmetric mean curvature flow of genus-1 surfaces
A filtered two-step variational integrator for charged-particle dynamics in a normal or strong magnetic field
On the best accuracy using the $h$-adaptive finite element refinement
Maximum Bound Principle and Bound Preserving ETD schemes for a Phase-Field Model of Tumor Growth with Extracellular Matrix Degradation
Adaptive stochastic Galerkin finite element methods: Optimality and non-affine coefficients
Least-Squares Finite Element Methods for nonlinear problems: A unified framework
Micro-Macro Coupling for Optimizing Scaffold Mediated Bone Regeneration
High-Order and Energy-Stable Implicit-Explicit Relaxation Runge-Kutta Schemes for Gradient Flows
Parameter-robust preconditioner for Stokes-Darcy coupled problem with Lagrange multiplier
Kernel compensation method for Maxwell eigenproblem with mimetic finite difference discretization
Empirical Hyper Element Integration Method (EHEIM) with Unified Integration Criteria for Efficient Hyper Reduced FE$^2$ Simulations
Asymptotic-preserving and positivity-preserving discontinuous Galerkin method for the semiconductor Boltzmann equation in the diffusive scaling
Characteristic boundary conditions for Hybridizable Discontinuous Galerkin methods
Enhanced gradient recovery-based a posteriori error estimator and adaptive finite element method for elliptic equations
A comparative study of calibration techniques for finite strain elastoplasticity: Numerically-exact sensitivities for FEMU and VFM
Adaptive refinement in defeaturing problems via an equilibrated flux a posteriori error estimator
Global Bounds for the Error in Solutions of Linear Hyperbolic Systems due to Inaccurate Boundary Geometry
A Semi-Lagrangian scheme for Hamilton-Jacobi-Bellman equations with Dirichlet boundary conditions
Second order divergence constraint preserving schemes for two-fluid relativistic plasma flow equations
Consistent splitting SAV schemes for finite element approximations of incompressible flows
Technical Note: Continuum Theory of Mixture for Three-phase Thermomechanical Model of Fiber-reinforced Aerogel Composites
The MINI mixed virtual element for the Stokes equation
ConicCurv: A curvature estimation algorithm for planar polygons
Inverse Lax-Wendroff boundary treatment for solving conservation laws with finite difference HWENO methods
A posteriori error estimates for the finite element discretization of second-order PDEs set in unbounded domains
A high order multigrid-preconditioned immersed interface solver for the Poisson equation with boundary and interface conditions