Speaker
Ngoc Tien Tran
Description
Solutions to partial differential equations (PDE) of second-order in nondivergence form are, in general, difficult to approximate by finite element methods due to the lack of a variational formulation. In such cases, minimal residual methods may be the method of choice due to their wide accessibility. The residual of this paper stems from the Alexandrov--Bakelman--Pucci maximum principle for the Pucci extremal operators. The minimization of this residual in suitable finite element spaces leads to a sequence of discrete approximations that converges uniformly to the exact strong solution, provided the PDE satisfies further assumptions. Since only local regularity is required, the domain is allowed to be non-convex and non-smooth.
