Optimal Error Estimates for Semidiscrete Galerkin Approximations to Multi-dimensional Sobolev Equations with Burgers’ Type Nonlinearity

2018 ◽  
pp. 209-227
Author(s):  
Ambit K. Pany ◽  
Sudeep Kundu
Keyword(s):  
Error Estimates ◽  
Optimal Error Estimates ◽  
Optimal Error ◽  
Sobolev Equations ◽  
Galerkin Approximations

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 A stabilized coupled method and its optimal error estimates for elliptic interface problems

2019 ◽  
Vol 2019 (1) ◽  
Author(s):  
Jiaping Yu ◽  
Feng Shi ◽  
Jianping Zhao
Keyword(s):  
Error Estimates ◽  
Numerical Experiments ◽  
Interface Problems ◽  
Optimal Error Estimates ◽  
Computational Stability ◽  
Optimal Error ◽  
Stabilized Method ◽  
Elliptic Interface Problems ◽  
Coupled Method

Abstract In this paper, we present a stabilized coupled algorithm for solving elliptic interface problems, mainly by introducing the jump of the solutions along the interface. A framework of theoretical proofs is provided to show the optimal error estimates of this stabilized method. Several numerical experiments are carried out to demonstrate the computational stability and effectiveness of the method.

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