Error analysis of discrete conservation laws for Hamiltonian PDEs under the central box discretizations

2009 ◽  
Vol 211 (1) ◽  
pp. 155-166
Author(s):  
Jian Wang
Keyword(s):  
Error Analysis ◽  
Conservation Laws ◽  
Hamiltonian Pdes ◽  
Discrete Conservation Laws

Conformal conservation laws and geometric integration for damped Hamiltonian PDEs

2013 ◽  
Vol 232 (1) ◽  
pp. 214-233 ◽  
Author(s):  
Brian E. Moore ◽  
Laura Noreña ◽  
Constance M. Schober
Keyword(s):  
Conservation Laws ◽  
Geometric Integration ◽  
Hamiltonian Pdes

scholarly journals Simple bespoke preservation of two conservation laws

2018 ◽  
Vol 40 (2) ◽  
pp. 1294-1329 ◽  
Author(s):  
Gianluca Frasca-Caccia ◽  
Peter Ellsworth Hydon
Keyword(s):  
Finite Difference ◽  
Conservation Laws ◽  
Vries Equation ◽  
Finite Difference Methods ◽  
Nonlinear Heat Equation ◽  
Finite Difference Schemes ◽  
Simplified Approach ◽  
Numerical Tests ◽  
Difference Methods ◽  
Discrete Conservation Laws

Abstract Conservation laws are among the most fundamental geometric properties of a partial differential equation (PDE), but few known finite difference methods preserve more than one conservation law. All conservation laws belong to the kernel of the Euler operator, an observation that was first used recently to construct approximations symbolically that preserve two conservation laws of a given PDE. However, the complexity of the symbolic computations has limited the effectiveness of this approach. The current paper introduces some key simplifications that make the symbolic–numeric approach feasible. To illustrate the simplified approach we derive bespoke finite difference schemes that preserve two discrete conservation laws for the Korteweg–de Vries equation and for a nonlinear heat equation. Numerical tests show that these schemes are robust and highly accurate compared with others in the literature.

Sign in / Sign up

Export Citation Format

Share Document