A weighted hybridizable discontinuous Galerkin method for drift-diffusion problems
DOI10.1007/s10915-024-02481-warXiv2211.02508OpenAlexW4393044936MaRDI QIDQ6120013
Wenyu Lei, Luca Heltai, Stefano Piani, Patricio Farrell, Nella Rotundo
Publication date: 25 March 2024
Published in: Journal of Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/2211.02508
finite element methodsdiscontinuous Galerkin methodsconvection-diffusion equationsexponential fitting methodsdrift-diffusion problemshybrid methods weighted norms
Error bounds for boundary value problems involving PDEs (65N15) 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) Statistical mechanics of semiconductors (82D37) Electromagnetic theory (general) (78A25) Motion of charged particles (78A35) Finite volume methods for boundary value problems involving PDEs (65N08)
Cites Work
- Unnamed Item
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- A finite volume scheme for convection-diffusion equations with nonlinear diffusion derived from the Scharfetter-Gummel scheme
- The finite volume-complete flux scheme for advection-diffusion-reaction equations
- Numerical simulation of semiconductor devices
- An existence result for elliptic partial differential-algebraic equations arising in semiconductor modeling
- Partial differential equations. III: Nonlinear equations.
- An implicit high-order hybridizable discontinuous Galerkin method for linear convection-diffusion equations
- Computational and analytical comparison of flux discretizations for the semiconductor device equations beyond Boltzmann statistics
- Theory and practice of finite elements.
- Long-time behaviour of hybrid finite volume schemes for advection-diffusion equations: linear and nonlinear approaches
- The \textsc{deal.II} finite element library: design, features, and insights
- An HDG method for the time-dependent drift-diffusion model of semiconductor devices
- Uniform second order convergence of a complete flux scheme on unstructured 1D grids for a singularly perturbed advection-diffusion equation and some multidimensional extensions
- The complete flux scheme -- error analysis and application to plasma simulation
- The \texttt{deal.II} library, Version 9.3
- A finite-volume scheme for a spinorial matrix drift-diffusion model for semiconductors
- A Discontinuous-Skeletal Method for Advection-Diffusion-Reaction on General Meshes
- Elliptic Partial Differential-Algebraic Multiphysics Models in Electrical Network Design
- A superconvergent LDG-hybridizable Galerkin method for second-order elliptic problems
- Superconvergent discontinuous Galerkin methods for second-order elliptic problems
- Discretization of heterogeneous and anisotropic diffusion problems on general nonconforming meshes SUSHI: a scheme using stabilization and hybrid interfaces
- A Hybridizable Discontinuous Galerkin Method for Steady-State Convection-Diffusion-Reaction Problems
- IMPROVED FINITE-DIFFERENCE SCHEME FOR THE SOLUTION OF CONVECTION-DIFFUSION PROBLEMS WITH THE SIMPLEN ALGORITHM
- Robust Numerical Methods for Singularly Perturbed Differential Equations
- Unified Hybridization of Discontinuous Galerkin, Mixed, and Continuous Galerkin Methods for Second Order Elliptic Problems
- Some Error Estimates for the Box Method
- Two-Dimensional Exponential Fitting and Applications to Drift-Diffusion Models
- Discretization of the stationary convection-diffusion-reaction equation
- AN EXPONENTIAL FITTING SCHEME FOR THE ELECTROTHERMAL DEVICE EQUATIONS SPECIFICALLY FOR THE SIMULATION OF AVALANCHE GENERATION
- Unified Analysis of Discontinuous Galerkin Methods for Elliptic Problems
- TetGen, a Delaunay-Based Quality Tetrahedral Mesh Generator
- A UNIFIED APPROACH TO MIMETIC FINITE DIFFERENCE, HYBRID FINITE VOLUME AND MIXED FINITE VOLUME METHODS
- A minimal stabilisation procedure for mixed finite element methods
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