Implementation of a novel element-by-element finite element method on the hypercube

Galerkin method for a nonlinear parabolic–elliptic system with nonlinear mixed boundary conditions

“…T h i s method has the advantage of massive parallelism. For preliminary studies of this new method see Layton and Rabier [22,23], and Sunmonu [29].…”

“…Other theoretical results on the existence and uniqueness to the steady state analogue of (1)-(2) can be found in Sunmonu [30] for g 0, and in Cimatti and Prodi [5] for the pure Dirichlet boundary conditions and Cimatti [3] for the mixed boundary condition with g ( x , u ) = 0. For numerical experiments, see for example, the works of Troyani [32] for the aluminum reduction cell, Westbrook [33], Sunmonu [29] and Flynn [I81 for the thermistor problem. The analysis presented in this article extends the theoretical convergence results cited above to include the nonlinear term Q = Q ( x , t , u , V P ) and the nonlinear third kind boundary conditions, and also provide theoretical foundation for the numerical experiments discussed in Sunmonu theoretical foundation for the numerical experiments discussed in Sunmonu [28] and the previously cited papers.…”

Thermal Convection in a Heated-Block Duct with Periodic Boundary Conditions by Element-by-Element Treatment

“…He then used the EBE-CG calculation matrix to show that the latter required less numerical storage and CPU time to calculate large-scale flow fields. Li et al [17] and Sunmonu [18] employed the EBE method to decrease the matrix, which shortened the computer's calculation time. Reddy et al [19] used the EBE numerical architecture to reduce the number of iterations during computation when calculating the flow field of viscous incompressible fluids by integrating two iteration methods with a multigrid approach.…”