A general framework for finding energy dissipative/conservative H~1-Galerkin schemes and their underlying H~1-weak forms for nonlinear evolution equations

摘要

A general framework for constructing energy dissipative or conservative Galerkin schemes for time-dependent partial differential equations (PDEs) is presented. The framework embraces a variety of dissipative and conservative PDEs with variational structure. An advantageous feature is that implementation of the resulting scheme requires only P1 elements. The schemes and their underlying H~1-weak forms are derived from the concept of formal weak form and an L~2-projection technique.