Energy Method

A functional-analytic technique that obtains a priori bounds for solutions of differential or evolution equations by multiplying equations by test functions (often the solution or its derivatives) and integrating to produce conserved or dissipative energy inequalities.

A technique that constructs an energy-like functional (often norm-squared or a conserved/dissipated quadratic form), differentiates it along solutions, and uses sign/coercivity and integral inequalities to obtain a priori estimates for differential equations.