Pointwise a Posteriori Error Bounds for Blow-Up in the Semilinear Heat Equation
DOI10.1137/19M1264758zbMath1473.65202arXiv1802.07757OpenAlexW3088811601MaRDI QIDQ4970509
Publication date: 14 October 2020
Published in: SIAM Journal on Numerical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1802.07757
Nonlinear parabolic equations (35K55) Heat equation (35K05) Finite element, Rayleigh-Ritz and Galerkin methods for boundary value problems involving PDEs (65N30) Finite difference methods for initial value and initial-boundary value problems involving PDEs (65M06) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Blow-up in context of PDEs (35B44) Semilinear parabolic equations (35K58)
Related Items (2)
Uses Software
Cites Work
- Unnamed Item
- Unnamed Item
- Maximum-norm a posteriori error estimates for singularly perturbed elliptic reaction-diffusion problems
- The \texttt{deal.II} library, version 8.4
- Blow-up theories for semilinear parabolic equations
- An adaptive time step procedure for a parabolic problem with blow-up
- Numerical verification for existence of a global-in-time solution to semilinear parabolic equations
- Galerkin finite element methods for parabolic problems
- Totally discrete explicit and semi-implicit Euler methods for a blow-up problem in several space dimensions
- A study of moving mesh PDE methods for numerical simulation of blowup in reaction diffusion equations
- A posteriori error estimates and maximal regularity for approximations of fully nonlinear parabolic problems in Banach spaces
- Improved maximum-norm a posteriori error estimates for linear and semilinear parabolic equations
- \(hp\)-adaptive Galerkin time stepping methods for nonlinear initial value problems
- A posteriori error analysis for time-dependent Ginzburg-Landau type equations
- The effect of mesh modification in time on the error control of fully discrete approximations for parabolic equations
- A Liouville theorem for vector-valued nonlinear heat equations and applications
- Continuous and discontinuous Galerkin time stepping methods for nonlinear initial value problems with application to finite time blow-up
- Pointwise a posteriori error estimates for monotone semi-linear equations
- Blow-up results for a strongly perturbed semilinear heat equation: theoretical analysis and numerical method
- Maximum Norm A Posteriori Error Estimation for Parabolic Problems Using Elliptic Reconstructions
- On a posteriori error control for the Allen-Cahn problem
- Adaptive discontinuous Galerkin methods for nonstationary convection-diffusion problems
- Adaptivity and Blow-Up Detection for Nonlinear Evolution Problems
- Analysis for Time Discrete Approximations of Blow-up Solutions of Semilinear Parabolic Equations
- Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems
- deal.II—A general-purpose object-oriented finite element library
- A Posteriori Error Estimates in the Maximum Norm for Parabolic Problems
- A rescaling algorithm for the numerical calculation of blowing-up solutions
- Mesh Modification for Evolution Equations
- Elliptic Reconstruction and a Posteriori Error Estimates for Parabolic Problems
- Revealing new dynamical patterns in a reaction–diffusion model with cyclic competition via a novel computational framework
- An adaptive space-time Newton–Galerkin approach for semilinear singularly perturbed parabolic evolution equations
- Moving Mesh Methods for Problems with Blow-Up
- A posteriorierror control for the Allen–Cahn problem: circumventing Gronwall's inequality
- A Method of Verified Computations for Solutions to Semilinear Parabolic Equations Using Semigroup Theory
This page was built for publication: Pointwise a Posteriori Error Bounds for Blow-Up in the Semilinear Heat Equation