A general framework for finding energy dissipative/conservative \(H^1\)-Galerkin schemes and their underlying \(H^1\)-weak forms for nonlinear evolution equations
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.
dissipation conservation \(l^2\)-projection discrete partial derivative method galerkin method structure-preserving integration discrete gradient method 65m60