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Numerical preservation of local conservation laws

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GCS - Geometry, compatibility and structure preservation in computational differential equations

In the numerical treatment of partial differential equations (PDEs), the benefits of preserving global integral invariants are well-known. Preserving the underlying local conservation law gives, in general, a stricter constraint than conserving the global invariant obtained by integrating it in space. Conservation laws, in fact, hold throughout the domain and are satisfied by all solutions, independently of initial and boundary conditions. A new approach that uses symbolic algebra to develop bespoke finite difference schemes that preserve multiple local conservation laws has been recently applied to PDEs with polynomial nonlinearity. The talk illustrates this new strategy using some well-known equations as benchmark examples and shows comparisons between the obtained schemes and other integrators known in literature.




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