[图书][B] Finite elements II
A Ern, JL Guermond - 2021 - Springer
The mathematization of all sciences, the fading of traditional scientific boundaries, the
impact of computer technology, the growing importance of computer modelling and the …
impact of computer technology, the growing importance of computer modelling and the …
Breaking spaces and forms for the DPG method and applications including Maxwell equations
C Carstensen, L Demkowicz… - Computers & Mathematics …, 2016 - Elsevier
Abstract Discontinuous Petrov–Galerkin (DPG) methods are made easily implementable
using “broken” test spaces, ie, spaces of functions with no continuity constraints across mesh …
using “broken” test spaces, ie, spaces of functions with no continuity constraints across mesh …
A spacetime DPG method for the Schrodinger equation
L Demkowicz, J Gopalakrishnan, S Nagaraj… - SIAM Journal on …, 2017 - SIAM
A spacetime discontinuous Petrov--Galerkin (DPG) method for the linear time-dependent
Schrödinger equation is proposed. The spacetime approach is particularly attractive for …
Schrödinger equation is proposed. The spacetime approach is particularly attractive for …
[PDF][PDF] Discontinuous Petrov–Galerkin (DPG) method
L Demkowicz, J Gopalakrishnan - ICES report, 2015 - pdx.edu
The article reviews fundamentals of Discontinuous Petrov-Galerkin (DPG) Method with
Optimal Test Functions. The main idea admits three different interpretations: a Petrov …
Optimal Test Functions. The main idea admits three different interpretations: a Petrov …
Construction of DPG Fortin operators for second order problems
S Nagaraj, S Petrides, LF Demkowicz - Computers & Mathematics with …, 2017 - Elsevier
The use of “ideal” optimal test functions in a Petrov–Galerkin scheme guarantees the
discrete stability of the variational problem. However, in practice, the computation of the …
discrete stability of the variational problem. However, in practice, the computation of the …
Recent advances in least-squares and discontinuous Petrov–Galerkin finite element methods
F Bertrand, L Demkowicz, J Gopalakrishnan… - … Methods in Applied …, 2019 - degruyter.com
Least-squares (LS) and discontinuous Petrov–Galerkin (DPG) finite element methods are an
emerging methodology in the computational partial differential equations with unconditional …
emerging methodology in the computational partial differential equations with unconditional …
Robust DPG Test Spaces and Fortin Operators—The and Cases
At the fully discrete setting, stability of the discontinuous Petrov–Galerkin (DPG) method with
optimal test functions requires local test spaces that ensure the existence of Fortin operators …
optimal test functions requires local test spaces that ensure the existence of Fortin operators …
Low-order discontinuous Petrov--Galerkin finite element methods for linear elasticity
C Carstensen, F Hellwig - SIAM Journal on Numerical Analysis, 2016 - SIAM
This paper analyzes lowest-order discontinuous Petrov--Galerkin (dPG) finite element
methods (FEM) for the Navier--Lamé equations with different norms and side restrictions …
methods (FEM) for the Navier--Lamé equations with different norms and side restrictions …
An ultraweak formulation of the Kirchhoff–Love plate bending model and DPG approximation
We develop and analyze an ultraweak variational formulation for a variant of the Kirchhoff–
Love plate bending model. Based on this formulation, we introduce a discretization of the …
Love plate bending model. Based on this formulation, we introduce a discretization of the …
MINRES for second-order PDEs with singular data
Minimum residual methods such as the least-squares finite element method (FEM) or the
discontinuous Petrov--Galerkin (DPG) method with optimal test functions usually exclude …
discontinuous Petrov--Galerkin (DPG) method with optimal test functions usually exclude …