Structure preserving polytopal discontinuous Galerkin methods for the numerical modeling of neurodegenerative diseases

DOI10.1007/s10915-024-02581-7MaRDI QIDQ6571384

Unnamed Author, Francesca Bonizzoni, Paola Francesca Antonietti

Publication date: 12 July 2024

Published in: Journal of Scientific Computing (Search for Journal in Brave)

zbMATH Keywords

discontinuous Galerkinneurodegenerative diseasepolytopal methodsstructure preserving methods

Mathematics Subject Classification ID

Neural biology (92C20) PDEs in connection with biology, chemistry and other natural sciences (35Q92) Stability and convergence of numerical methods for boundary value problems involving PDEs (65N12) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Numerical solution of discretized equations for boundary value problems involving PDEs (65N22)

Cites Work

• Unnamed Item
• \texttt{PolyMesher}: a general-purpose mesh generator for polygonal elements written in Matlab
• An explicit positivity-preserving finite-difference scheme for the classical Fisher-Kolmogorov-Petrovsky-Piscounov equation
• On the constants in \(hp\)-finite element trace inverse inequalities.
• Numerical analysis of a robust free energy diminishing finite volume scheme for parabolic equations with gradient structure
• The interplay of biochemical and biomechanical degeneration in Alzheimer's disease
• Numerical models for differential problems
• A local domain boundary element method for solving the nonlinear Fisher KPP diffusion-reaction equation
• Robust interior penalty discontinuous Galerkin methods
• A structure-preserving discontinuous Galerkin scheme for the Fisher-KPP equation
• Estimating the extent of glioblastoma invasion. Approximate stationalization of anisotropic advection-diffusion-reaction equations in the context of glioblastoma invasion
• The hybrid high-order method for polytopal meshes. Design, analysis, and applications
• The wave of advance of advantageous genes.
• Partial Differential Equations in Action
• Entropy Methods for Diffusive Partial Differential Equations
• A discontinuous Galerkin method with weighted averages for advection-diffusion equations with locally small and anisotropic diffusivity
• A Priori Error Estimates for Finite Element Methods Based on Discontinuous Approximation Spaces for Elliptic Problems
• Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
• ℎ𝑝-version discontinuous Galerkin methods on essentially arbitrarily-shaped elements
• Invariant-Domain-Preserving High-Order Time Stepping: I. Explicit Runge--Kutta Schemes
• High–order Discontinuous Galerkin Methods on Polyhedral Grids for Geophysical Applications: Seismic Wave Propagation and Fractured Reservoir Simulations
• Mathematical Modeling of the Human Brain
• Agglomeration of polygonal grids using graph neural networks with applications to multigrid solvers
• Discontinuous Galerkin methods for Fisher-Kolmogorov equation with application to \(\alpha\)-synuclein spreading in Parkinson's disease
• Structure preservation in high-order hybrid discretisations of potential-driven advection-diffusion: linear and nonlinear approaches
• The role of clearance in neurodegenerative diseases

Related Items (2)

Discontinuous Galerkin approximations of the heterodimer model for protein-protein interaction ⋮ Arbitrary order positivity preserving finite-volume schemes for 2D elliptic problems

This page was built for publication: Structure preserving polytopal discontinuous Galerkin methods for the numerical modeling of neurodegenerative diseases