Eliminating Gibbs phenomena: a non-linear Petrov-Galerkin method for the convection-diffusion-reaction equation
From MaRDI portal
Publication:2194807
DOI10.1016/j.camwa.2020.03.025zbMath1447.65146arXiv1908.00996OpenAlexW3032869507MaRDI QIDQ2194807
Paul Houston, Sarah Roggendorf, Kristoffer G. Van Der Zee
Publication date: 7 September 2020
Published in: Computers \& Mathematics with Applications (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1908.00996
Related Items
Gibbs phenomena for Lq-best approximation in finite element spaces, A priori error analysis of high-order LL* (FOSLL*) finite element methods, An \(L^p\)-DPG method with application to 2D convection-diffusion problems, Battling Gibbs phenomenon: on finite element approximations of discontinuous solutions of PDEs, A priori error estimates for a semi‐Lagrangian unified finite element method for coupled Darcy‐transport problems, A uniformly convergent defect correction method for parabolic singular perturbation problems with a large delay, Analysis of a Galerkin-characteristic finite element method for convection-diffusion problems in porous media, An \(L^p\)-DPG method for the convection-diffusion problem, Discretization of Linear Problems in Banach Spaces: Residual Minimization, Nonlinear Petrov--Galerkin, and Monotone Mixed Methods
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- A robust DPG method for convection-dominated diffusion problems. II: Adjoint boundary conditions and mesh-dependent test norms
- A class of discontinuous Petrov-Galerkin methods. IV: The optimal test norm and time-harmonic wave propagation in 1D
- Finite element methods for time-dependent convection-diffusion-reaction equations with small diffusion
- Automated solution of differential equations by the finite element method. The FEniCS book
- On the performance of SOLD methods for convection-diffusion problems with interior layers
- On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations. II: Analysis for \(P_{1}\) and \(Q_{1}\) finite elements
- Explicit and implicit FEM-FCT algorithms with flux linearization
- An optimal \(L_1\)-minimization algorithm for stationary Hamilton-Jacobi equations
- On spurious oscillations at layers diminishing (SOLD) methods for convection-diffusion equations. I: A review
- Functional analysis, Sobolev spaces and partial differential equations
- Nonoscillatory solution of the steady-state inviscid Burgers' equation by mathematical programming
- A Gibbs phenomenon for spline functions
- Non-oscillatory and non-diffusive solution of convection problems by the iteratively reweighted least-squares finite element method
- Flux correction tools for finite elements
- Numerical approximation of hyperbolic systems of conservation laws
- The Gibbs phenomenon for best \(L_ 1\)-trigonometric polynomial approximation
- The convection-diffusion-reaction equation in non-Hilbert Sobolev spaces: a direct proof of the inf-sup condition and stability of Galerkin's method
- The discrete-dual minimal-residual method (DDMRES) for weak advection-reaction problems in Banach spaces
- High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments
- A fast algorithm for solving first-order PDEs by \(L^1\)-minimization
- Hermes2D, a C++ library for rapid development of adaptive \(hp\)-FEM and \(hp\)-DG solvers
- Geometric properties of Banach spaces and nonlinear iterations
- High-resolution FEM--FCT schemes for multidimensional conservation laws
- A dual Petrov-Galerkin finite element method for the convection-diffusion equation
- A robust Petrov-Galerkin discretisation of convection-diffusion equations
- Adaptivity and variational stabilization for convection-diffusion equations
- Robust DPG Method for Convection-Dominated Diffusion Problems
- An analysis of the practical DPG method
- A class of discontinuous Petrov-Galerkin methods. II. Optimal test functions
- Robust Numerical Methods for Singularly Perturbed Differential Equations
- Solution of Steady-State, Two-Dimensional Conservation Laws by Mathematical Programming
- Finite Volume Methods for Hyperbolic Problems
- A Finite Element Technique for Solving First-Order PDEs inLp
- Solution of Steady-State One-Dimensional Conservation Laws by Mathematical Programming
- A Petrov-Galerkin discretization with optimal test space of a mild-weak formulation of convection-diffusion equations in mixed form
- $L^1$-Approximation of Stationary Hamilton–Jacobi Equations
- Stabilized Galerkin approximation of convection-diffusion-reaction equations: discrete maximum principle and convergence
- An Overview of the Discontinuous Petrov Galerkin Method
