We develop a new mixed formulation for the numerical solution of second-order elliptic problems. This new formulation expands the standard mixed formulation in the sense that three variables are explicitly treated: the scalar unknown, its gradient, and its ux (the coeecient times the gradient). Based on this formulation, mixed nite element approximations of the second-order elliptic problems ar...

Least-squares finite element methods are an attractive class of methods for the numerical solution of partial differential equations. They are motivated by the desire to recover, in general settings, the advantageous features of Rayleigh–Ritz methods such as the avoidance of discrete compatibility conditions and the production of symmetric and positive definite discrete systems. The methods are...

We introduce a hybrid method to couple continuous Galerkin finite element methods and high-order difference in nonconforming multiblock fashion. The aim is optimize computational efficiency when complex geometries are present. proposed coupling technique requires minimal changes the existing schemes while maintaining strict stability, accuracy, energy conservation. Results demonstrated on linea...