We give an overview of multilevel methods, such as V-cycle multigrid and BPX
preconditioner, for solving various partial differential equations (including H (grad), H (curl) …

In this paper we present a family of scalable preconditioners for matrices arising in the
discretization of H(div) problems using the lowest order Raviart--Thomas finite elements. Our …

Since their emergence in the early 1950s, finite element methods have become one of the
most versatile and powerful methodologies for the approximate numerical solution of partial …

We generalize the construction and analysis of auxiliary space preconditioners to the n-
dimensional finite element subcomplex of the de Rham complex. These preconditioners are …

We develop and analyze least-squares finite element methods for two complementary div-
curl elliptic boundary value problems. The first one prescribes the tangential component of …

This paper is devoted to study of an auxiliary spaces preconditioner for H (div) systems and
its application in the mixed formulation of second order elliptic equations. Extensive …

This paper gives an overview of some recent works by the author and collaborators on
numerical methods for partial differential equations. One focus is on the development and …