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We lay out a program for constructing discontinuous Petrov–Galerkin (DPG) schemes
having test function spaces that are automatically computable to guarantee stability. Given a …

We consider the application of least-squares variational principles to the numerical solution
of partial differential equations. Our main focus is on the development of least-squares finite …

We investigate the use of least-squares methods to approximate the Helmholtz equation.
The basis used in the discrete method consists of solutions of the Helmholtz equation (either …

This paper is concerned with the design and analysis of adaptive wavelet methods for
systems of operator equations. Its main accomplishment is to extend the range of …

This paper develops a least-squares functional that arises from recasting general second-
order uniformly elliptic partial differential equations in n=2 or 3 dimensions as a system of …

We continue our theoretical and numerical study on the Discontinuous Petrov–Galerkin
method with optimal test functions in context of 1D and 2D convection-dominated diffusion …

This book is the third volume of a three-part textbook suitable for graduate coursework,
professional engineering and academic research. It is also appropriate for graduate flipped …

We give an error analysis of the recently developed DPG method applied to solve the
Poisson equation and a convection-diffusion problem. We prove that the method is …

Residual minimization is a widely used technique for solving Partial Differential Equations in
variational form. It minimizes the dual norm of the residual, which naturally yields a saddle …