An optimal adaptive wavelet method for First Order System Least Squares
Provides a general framework for solving a wide class of PDEs with optimal complexity, benefiting computational science and engineering.
The authors show that any well-posed 2nd order PDE can be reformulated as a well-posed first order least squares system, and then solved by an adaptive wavelet solver with optimal computational complexity. Applications include second order elliptic PDEs with general inhomogeneous boundary conditions and stationary Navier-Stokes equations.
In this paper, it is shown that any well-posed 2nd order PDE can be reformulated as a well-posed first order least squares system. This system will be solved by an adaptive wavelet solver in optimal computational complexity. The applications that are considered are second order elliptic PDEs with general inhomogeneous boundary conditions, and the stationary Navier-Stokes equations.