Discontinuous Galerkin Methods for Weakly Coupled Hyperbolic MultiDomain Problems
DOI10.1137/16M1089332zbMath1375.65134OpenAlexW2758301413MaRDI QIDQ5364200
Mengping Zhang, Qingyuan Liu, Chi-Wang Shu
Publication date: 4 October 2017
Published in: SIAM Journal on Scientific Computing (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1137/16m1089332
stabilitynumerical resultserror estimatesRunge-Kutta discontinuous Galerkin methoddiscontinuous fluxesbiological cell proliferation modelhyperbolic multidomain problem
Initial-boundary value problems for second-order hyperbolic equations (35L20) Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs (65M12) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Cell biology (92C37) Method of lines for initial value and initial-boundary value problems involving PDEs (65M20)
Cites Work
- Unnamed Item
- Unnamed Item
- Positivity-preserving high order finite difference WENO schemes for compressible Euler equations
- Stability analysis and a priori error estimate of explicit Runge-Kutta discontinuous Galerkin methods for correlated random walk with density-dependent turning rates
- A relaxation scheme for continuous sedimentation in ideal clarifier-thickener units
- On maximum-principle-satisfying high order schemes for scalar conservation laws
- Efficient implementation of essentially nonoscillatory shock-capturing schemes
- TVB Runge-Kutta local projection discontinuous Galerkin finite element method for conservation laws. III: One-dimensional systems
- The Runge-Kutta discontinuous Galerkin method for conservation laws. I: Multidimensional systems
- Runge--Kutta discontinuous Galerkin methods for convection-dominated problems
- Cauchy problem for multiscale conservation laws: application to structured cell populations
- Conservation laws with discontinuous flux: a short introduction
- Multi-scale modeling of the follicle selection process in the ovary
- Superconvergence of the Local Discontinuous Galerkin Method for Elliptic Problems on Cartesian Grids
- Strong Stability-Preserving High-Order Time Discretization Methods
- Coupling Techniques for Nonlinear Hyperbolic Equations. III. The Well-Balanced Approximation of Thick Interfaces
- ANALYSIS AND APPROXIMATION OF A SCALAR CONSERVATION LAW WITH A FLUX FUNCTION WITH DISCONTINUOUS COEFFICIENTS
- Analysis of a Local Discontinuous Galerkin Method for Linear Time-Dependent Fourth-Order Problems
- Numerical simulation of the selection process of the ovarian follicles
- The Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws. IV: The Multidimensional Case
- Multiscale Modeling of Follicular Ovulation as a Reachability Problem
- TVB Runge-Kutta Local Projection Discontinuous Galerkin Finite Element Method for Conservation Laws II: General Framework
- Error Estimates to Smooth Solutions of Runge--Kutta Discontinuous Galerkin Methods for Scalar Conservation Laws
- Multiscale modelling of endocrine systems: new insight on the gonadotrope axis
- Stability Analysis and A Priori Error Estimates of the Third Order Explicit Runge–Kutta Discontinuous Galerkin Method for Scalar Conservation Laws
- A Numerical Method for Transport Equations with Discontinuous Flux Functions: Application to Mathematical Modeling of Cell Dynamics
