Results 261 to 270 of about 28,174,747 (313)
Some of the next articles are maybe not open access.
SIAM Journal on Numerical Analysis, 1989
This article presents a new method of integrating evolution differential equations—the non-linear Galerkin method—that is well adapted to the long-term integration of such equations.While the usual Galerkin method can be interpreted as a projection of the considered equation on a linear space, the methods considered here are related to the projection ...
Roger Temam, Martine Marion
openaire +2 more sources
This article presents a new method of integrating evolution differential equations—the non-linear Galerkin method—that is well adapted to the long-term integration of such equations.While the usual Galerkin method can be interpreted as a projection of the considered equation on a linear space, the methods considered here are related to the projection ...
Roger Temam, Martine Marion
openaire +2 more sources
A new weak Galerkin finite element method for the Helmholtz equation
, 2015An absolutely stable weak Galerkin finite element method is introduced and analyzed for the Helmholtz equation. This means that the stability and well posedness of the method for any wave number k can be derived without mesh size constraint.
Lin Mu, Junping Wang, X. Ye
semanticscholar +1 more source
A Low-Storage Curvilinear Discontinuous Galerkin Method for Wave Problems
SIAM Journal on Scientific Computing, 2013The low-storage curvilinear discontinuous Galerkin (LSC-DG) method reduces the storage requirements for solving symmetric and linear linear symmetric conservation laws in curvilinear domains when compared to the standard discontinuous Galerkin method. We
T. Warburton
semanticscholar +1 more source
A Galerkin method for Stefan problems
Applied Mathematics and Computation, 1992The one-dimensional Stefan problem is transformed to a convection- diffusion problem on a fixed interval. This transformed problem is then solved by a Galerkin method based on piecewise-linear splines. The algorithm is tested on a standard example for which an analytic solution is known.
openaire +3 more sources
A Note on the Galerkin Method's Stability
Mathematische Nachrichten, 1995AbstractNumerical stability of the Galerkin method for some class of semilinear evolution equations is studied. The stability is established in thelp(1 <p < ∞) norms. Our results are applied to the special coordinate systems. All the conditions of the stability theorems proved in this note may be readily verifiable in practice for them.
openaire +2 more sources
2020
Before we can understand the nuances of the various methods for discretizing nonlinear partial differential equations in space, we must first realize the choices that we have at our disposal. We can categorize the possible methods as follows: 1. methods that use the differential form of the equations and 2.
openaire +2 more sources
Before we can understand the nuances of the various methods for discretizing nonlinear partial differential equations in space, we must first realize the choices that we have at our disposal. We can categorize the possible methods as follows: 1. methods that use the differential form of the equations and 2.
openaire +2 more sources
1984
Galerkin methods have been used to solve problems in structural mechanics, dynamics, fluid flow, hydrodynamic stability, magnetohydrodynamics, heat and mass transfer, acoustics, microwave theory, neutron transport, etc. Problems governed by ordinary differential equations, partial differential equations, and integral equations have been investigated ...
openaire +2 more sources
Galerkin methods have been used to solve problems in structural mechanics, dynamics, fluid flow, hydrodynamic stability, magnetohydrodynamics, heat and mass transfer, acoustics, microwave theory, neutron transport, etc. Problems governed by ordinary differential equations, partial differential equations, and integral equations have been investigated ...
openaire +2 more sources
1984
When evaluated on a uniform grid, the Galerkin method produces symmetric formulae. Thus odd-order derivatives lead to zero coefficients associated with the node at which the function is centered. The steady, two-dimensional convection-diffusion equation is $$ u\frac{\partial T}{\partial x}~+~v\frac{\partial T}{\partial y}~-~D\left( \frac{{{\partial
openaire +2 more sources
When evaluated on a uniform grid, the Galerkin method produces symmetric formulae. Thus odd-order derivatives lead to zero coefficients associated with the node at which the function is centered. The steady, two-dimensional convection-diffusion equation is $$ u\frac{\partial T}{\partial x}~+~v\frac{\partial T}{\partial y}~-~D\left( \frac{{{\partial
openaire +2 more sources
2008
Die Formulierung des Randwert problems aus Kapitel 2 als Variationsproblem war muhsam, das Prinzip der Diskretisierung des Variationsproblems ist nun aber kurz darstellbar und lasst sich sehr allgemein formulieren.
openaire +2 more sources
Die Formulierung des Randwert problems aus Kapitel 2 als Variationsproblem war muhsam, das Prinzip der Diskretisierung des Variationsproblems ist nun aber kurz darstellbar und lasst sich sehr allgemein formulieren.
openaire +2 more sources
Galerkin and Collocation Methods
2018One method to numerically solve an equation consists in expanding the solution in terms of a set of known basis functions. These are the so-called “spectral” methods, where the main emphasis is placed on establishing procedures to obtain the expansion coefficients.
Thiago Carvalho Peixoto +2 more
openaire +2 more sources