This book offers a comprehensive presentation of some of the most successful and popular
domain decomposition preconditioners for finite and spectral element approximations of …

Two decades ago when we wrote Spectral Methods in Fluid Dynamics (1988), the subject
was still fairly novel. Motivated by the many favorable comments we have received and the …

These notes serve as an introduction to a subject of study in computational mathematics
referred to as domain decomposition methods. It concerns divide and conquer methods for …

Page 1 Trefftz and Collocation Methods ZC. Li, TT. Lu, WITPRESS HY. Hu & A. HD. Cheng
Page 2 TrefftzTrefftzTrefftzTrefftzTrefftz andandandandand …

Domain decomposition methods provide powerful preconditioners for the iterative solution of
the large systems of algebraic equations that arise in finite element or finite difference …

The efficient solution of discretizations of coupled systems of partial differential equations
(PDEs) is at the core of much of numerical simulation. Significant effort has been expended …

Effective relaxation methods are necessary for good multigrid convergence. For many
equations, standard Jacobi and Gauß–Seidel are inadequate, and more sophisticated …

Pavarino proved that the additive Schwarz method with vertex patches and a low-order
coarse space gives a $ p $-robust solver for symmetric and coercive problems. However, for …

In this article we address the question of efficiently solving the algebraic linear system of
equations arising from the discretization of a symmetric, elliptic boundary value problem …

This book deals with the general topic “Numerical solution of partial differential equations
(PDEs)” with a focus on adaptivity of discretizations in space and time. By and large …