An overview of the discontinuous Petrov Galerkin method
LF Demkowicz, J Gopalakrishnan - Recent Developments in …, 2014 - Springer
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A class of discontinuous Petrov–Galerkin methods. II. Optimal test functions
L Demkowicz, J Gopalakrishnan - Numerical Methods for …, 2011 - Wiley Online Library
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 …
having test function spaces that are automatically computable to guarantee stability. Given a …
Finite element methods of least-squares type
PB Bochev, MD Gunzburger - SIAM review, 1998 - SIAM
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 …
of partial differential equations. Our main focus is on the development of least-squares finite …
A least-squares method for the Helmholtz equation
P Monk, DQ Wang - Computer Methods in Applied Mechanics and …, 1999 - Elsevier
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 …
The basis used in the discrete method consists of solutions of the Helmholtz equation (either …
Adaptive wavelet methods II—beyond the elliptic case
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 …
systems of operator equations. Its main accomplishment is to extend the range of …
First-order system least squares for second-order partial differential equations: Part II
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 …
order uniformly elliptic partial differential equations in n=2 or 3 dimensions as a system of …
A class of discontinuous Petrov–Galerkin methods. Part III: Adaptivity
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 …
method with optimal test functions in context of 1D and 2D convection-dominated diffusion …
[图书][B] Finite elements III: first-order and time-dependent PDEs
A Ern, JL Guermond - 2021 - books.google.com
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 …
professional engineering and academic research. It is also appropriate for graduate flipped …
Analysis of the DPG method for the Poisson equation
L Demkowicz, J Gopalakrishnan - SIAM Journal on Numerical Analysis, 2011 - SIAM
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 …
Poisson equation and a convection-diffusion problem. We prove that the method is …
[HTML][HTML] A deep double Ritz method (D2RM) for solving partial differential equations using neural networks
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 …
variational form. It minimizes the dual norm of the residual, which naturally yields a saddle …