Unconditionally optimal error estimates of BDF2 Galerkin method for semilinear parabolic equation

2020 ◽  
Author(s):  
Huaijun Yang ◽  
Dongyang Shi ◽  
Li‐Tao Zhang
Keyword(s):  
Parabolic Equation ◽  
Galerkin Method ◽  
Error Estimates ◽  
Optimal Error Estimates ◽  
Semilinear Parabolic Equation ◽  
Optimal Error ◽  
Semilinear Parabolic

scholarly journals AnH1-Galerkin method for a Stefan problem with a quasilinear parabolic equation in non-divergence form

1987 ◽  
Vol 10 (2) ◽  
pp. 345-360 ◽  
Author(s):  
A. K. Pani ◽  
P. C. Das
Keyword(s):  
Parabolic Equation ◽  
Galerkin Method ◽  
Error Estimates ◽  
Stefan Problem ◽  
Single Phase ◽  
Quasilinear Parabolic Equation ◽  
Divergence Form ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Quasilinear Parabolic

Optimal error estimates inL2,H1andH2-norm are established for a single phase Stefan problem with quasilinear parabolic equation in non-divergence form by anH1-Galerkin procedure.

scholarly journals Optimal error estimates for fully discrete Galerkin approximations of semilinear parabolic equations

2018 ◽  
Vol 52 (6) ◽  
pp. 2307-2325 ◽  
Author(s):  
Dominik Meidner ◽  
Boris Vexler
Keyword(s):  
Error Estimates ◽  
Uniform Boundedness ◽  
Growth Conditions ◽  
Optimal Error Estimates ◽  
Semilinear Parabolic Equation ◽  
Optimal Error ◽  
Implicit Euler Scheme ◽  
Fully Discrete ◽  
Galerkin Approximations ◽  
Semilinear Parabolic

We consider a semilinear parabolic equation with a large class of nonlinearities without any growth conditions. We discretize the problem with a discontinuous Galerkin scheme dG(0) in time (which is a variant of the implicit Euler scheme) and with conforming finite elements in space. The main contribution of this paper is the proof of the uniform boundedness of the discrete solution. This allows us to obtain optimal error estimates with respect to various norms.

scholarly journals Error Estimates for Solutions of the Semilinear Parabolic Equation in Whole Space

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Xiaomei Hu
Keyword(s):  
Parabolic Equation ◽  
Initial Data ◽  
Error Estimates ◽  
Three Dimensional ◽  
Semilinear Parabolic Equation ◽  
Energy Methods ◽  
Analysis Technique ◽  
Whole Space ◽  
Fourier Analysis Technique ◽  
Semilinear Parabolic

This paper is focused on the error estimates for solutions of the three-dimensional semilinear parabolic equation with initial datau0∈L2(ℝ3). Employing the energy methods and Fourier analysis technique, it is proved that the error between the solution of the semilinear parabolic equation and that of linear heat equation has the behavior asO((1+t)−3/8).

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