Although the motto “when all else fails, integrate by parts” is applicable in a wide range of situations, the author first heard it in the context of the finite element method (FEM). The motto is relevant here since this method is based on the weak form of the PDE that one is trying to solve, and the weak form is obtained by multiplying the PDE by a test function and integrating by parts.
|Title of host publication||Unified Transform for Boundary Value Problems: Applications and Advances|
|Editors||Beatrice Pelloni, Athanassios Fokas|
|Publication status||Published - 2015|
Spence, E. (2015). Overview of Variational Formulations for Linear Elliptic PDEs. In B. Pelloni, & A. Fokas (Eds.), Unified Transform for Boundary Value Problems: Applications and Advances (pp. 93-160). SIAM.