\(\mathcal L\)-splines and viscosity limits for well-balanced schemes acting on linear parabolic equations
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Publication:683654
DOI10.1007/s10440-017-0122-5zbMath1380.65157OpenAlexW2749737838MaRDI QIDQ683654
Publication date: 8 February 2018
Published in: Acta Applicandae Mathematicae (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10440-017-0122-5
vanishing viscosityfundamental system of solutions\(\mathcal L\)-splineconstant/line perturbation method (C/L-PM)monotone well-balanced schemeparabolic cylinder functions (PCF)
Numerical computation using splines (65D07) Reaction-diffusion equations (35K57) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06)
Related Items (4)
Diffusive limits of 2D well-balanced schemes for kinetic models of neutron transport ⋮ A Two-Dimensional “Flea on the Elephant” Phenomenon and its Numerical Visualization ⋮ \(\mathscr{L}\)-splines as diffusive limits of dissipative kinetic models ⋮ Aliasing and two-dimensional well-balanced for drift-diffusion equations on square grids
Cites Work
- Unnamed Item
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- A tailored finite point method for a singular perturbation problem on an unbounded domain
- The structure of well-balanced schemes for Friedrichs systems with linear relaxation
- A uniformly convergent difference scheme for a semilinear singular perturbation problem
- Quasilinear hyperbolic systems
- An analytically oriented discretization technique for boundary value problems
- Singular perturbation methods for ordinary differential equations
- Global uniformly convergent schemes for a singularly perturbed boundary- value problem using patched base spline-functions
- A nonconforming finite element method for a singularly perturbed boundary value problem
- Numerical and asymptotic aspects of parabolic cylinder functions
- The random projection method for stiff multispecies detonation capturing
- Dirichlet-to-Neumann mappings and finite-differences for anisotropic diffusion
- A study of numerical methods for hyperbolic conservation laws with stiff source terms
- Fourth-order schemes of exponential type for singularly perturbed parabolic partial differential equations
- L-splines
- A new method for the solution of the Schrödinger equation
- On uniform approximation by certain generalized spline functions
- Error Estimates for Well-Balanced Schemes on Simple Balance Laws
- A SUGGESTED APPROACH TO FINITE-DIFFERENCE REPRESENTATION OF DIFFERENTIAL EQUATIONS,
- Generalized Finite Element Methods: Their Performance and Their Relation to Mixed Methods
- A Priori Estimates and Analysis of a Numerical Method for a Turning Point Problem
- On the Relation Between the Upwind-Differencing Schemes of Godunov, Engquist–Osher and Roe
- Computation of Exponential Splines
- Robust Numerical Methods for Singularly Perturbed Differential Equations
- Convergence of a Numerical Method for Solving Discontinuous Fokker–Planck Equations
- Error estimates for the Ultra Weak Variational Formulation of the Helmholtz equation
- Computing the real parabolic cylinder functions U ( a , x ), V ( a , x )
- A conservative, piecewise-steady difference scheme for transonic nozzle flow
- Strong Stability of Compact Discrete Boundary Value Problems via Exact Discretizations
- The algebraic theory approach for ordinary differential equations: Highly accurate finite differences
- Mode-Dependent Finite-Difference Discretization of Linear Homogeneous Differential Equations
- Direct solution procedure for solution of harmonic problems using complete, non-singular, Trefftz functions
- An Analysis of a Uniformly Accurate Difference Method for a Singular Perturbation Problem
- Nonlinear Singular Perturbation Problems and One Sided Difference Schemes
- Discrete Weighted Mean Approximation of a Model Convection-Diffusion Equation
- Homogenization of Scalar Conservation Laws with Oscillatory Forcing Terms
- On the Uniform Convergence of the Scharfetter–Gummel Discretization in One Dimension
- Application of an Ultra Weak Variational Formulation of Elliptic PDEs to the Two-Dimensional Helmholtz Problem
- A variational approach to splines
- Convergence of the $2 \times 2$ Godunov Method for a General Resonant Nonlinear Balance Law
- A Well-Balanced Scheme for the Numerical Processing of Source Terms in Hyperbolic Equations
- Computing Qualitatively Correct Approximations of Balance Laws
- Homogeneous difference schemes
- Approximation by local L-splines corresponding to a linear differential operator of the second order
- FUNDAMENTAL PROPERTIES OF GENERALIZED SPLINES
- A Correspondence Between Bayesian Estimation on Stochastic Processes and Smoothing by Splines
- On Boundary Value Problems for a Singularly Perturbed Differential Equation with a Turning Point
- Estimating the Eigenvalues of Sturm–Liouville Problems by Approximating the Differential Equation
- Fundamental systems of numerical schemes for linear convection-diffusion equations and their relationship to accuracy
- Trefftz method: An overview
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