3D domain decomposition method coupling conforming and nonconforming finite elements
This paper deals with the solution of problems involving partial differential equations in . For three dimensional case, methods are useful if they require neither domain boundary regularity nor regularity for the exact solution of the problem. A new domain decomposition method is therefore presented which uses low degree finite elements. The numerical approximation of the solution is easy, and optimal error bounds are obtained according to suitable norms.
We prove Hölder regularity of the gradient, up to the boundary for solutions of some fully-nonlinear, degenerate elliptic equations, with degeneracy coming from the gradient.