A weighted and balanced FEM for singularly perturbed reaction-diffusion problems
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Publication:2044541
DOI10.1007/s10092-021-00421-wzbMath1477.65231OpenAlexW3172514620MaRDI QIDQ2044541
Publication date: 9 August 2021
Published in: Calcolo (Search for Journal in Brave)
Full work available at URL: https://doi.org/10.1007/s10092-021-00421-w
Singular perturbations in context of PDEs (35B25) Reaction-diffusion equations (35K57) 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) Mesh generation, refinement, and adaptive methods for boundary value problems involving PDEs (65N50)
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Cites Work
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- Robust exponential convergence of \(hp\)-FEM in balanced norms for singularly perturbed reaction-diffusion equations
- Numerical solution of a two-dimensional singularly perturbed reaction-diffusion problem with discontinuous coefficients
- Layer-adapted meshes for reaction-convection-diffusion problems
- Elliptic partial differential equations of second order
- Error estimation in a balanced norm for a convection-diffusion problem with two different boundary layers
- Balanced-norm error estimates for sparse grid finite element methods applied to singularly perturbed reaction-diffusion problems
- Firedrake
- First-Order System Least Squares Finite-Elements for Singularly Perturbed Reaction-Diffusion Equations
- Differentiability Properties of Solutions of the Equation $ - \varepsilon ^2 \Delta u + ru = f(x,y)$ in a Square
- Convergence and stability in balanced norms of finite element methods on Shishkin meshes for reaction‐diffusion problems
- Robust Numerical Methods for Singularly Perturbed Differential Equations
- Maximum Norm A Posteriori Error Estimate for a 2D Singularly Perturbed Semilinear Reaction-Diffusion Problem
- A two-scale sparse grid method for a singularly perturbed reaction-diffusion problem in two dimensions
- Convection-Diffusion Problems
- A first-order system Petrov–Galerkin discretization for a reaction–diffusion problem on a fitted mesh
- A Balanced Finite Element Method for Singularly Perturbed Reaction-Diffusion Problems
- A Dual Finite Element Method for a Singularly Perturbed Reaction-Diffusion Problem
- A parameter robust numerical method for a two dimensional reaction-diffusion problem
- A Robust DPG Method for Singularly Perturbed Reaction-Diffusion Problems
- Anisotropic meshes and streamline‐diffusion stabilization for convection–diffusion problems