A new formulation and error analysis for vibrating dam–reservoir systems with upstream transmitting boundary conditions

2010 ◽  
Vol 329 (10) ◽  
pp. 1924-1953 ◽  
Author(s):  
Najib Bouaanani ◽  
Benjamin Miquel
Keyword(s):  
Error Analysis ◽  
Boundary Conditions ◽  
Dam Reservoir ◽  
Reservoir Systems ◽  
Transmitting Boundary ◽  
New Formulation

scholarly journals Abstract Nonconforming Error Estimates and Application to Boundary Penalty Methods for Diffusion Equations and Time-Harmonic Maxwell’s Equations

2018 ◽  
Vol 18 (3) ◽  
pp. 451-475 ◽  
Author(s):  
Alexandre Ern ◽  
Jean-Luc Guermond
Keyword(s):  
Error Analysis ◽  
Error Estimates ◽  
Material Properties ◽  
Maxwell’S Equations ◽  
Vector Fields ◽  
Maxwell's Equations ◽  
Heterogeneous Material ◽  
Test Functions ◽  
Time Harmonic ◽  
New Formulation

AbstractWe devise a novel framework for the error analysis of finite element approximations to low-regularity solutions in nonconforming settings where the discrete trial and test spaces are not subspaces of their exact counterparts. The key is to use face-to-cell extension operators so as to give a weak meaning to the normal or tangential trace on each mesh face individually for vector fields with minimal regularity and then to prove the consistency of this new formulation by means of some recently-derived mollification operators that commute with the usual derivative operators. We illustrate the technique on Nitsche’s boundary penalty method applied to a scalar diffusion equation and to the time-harmonic Maxwell’s equations. In both cases, the error estimates are robust in the case of heterogeneous material properties. We also revisit the error analysis framework proposed by Gudi where a trimming operator is introduced to map discrete test functions into conforming test functions. This technique also gives error estimates for minimal regularity solutions, but the constants depend on the material properties through contrast factors.

scholarly journals Self-consistent procedure including envelope function normalization for full-zone Schrödinger-Poisson problems with transmitting boundary conditions

2018 ◽  
Vol 124 (20) ◽  
pp. 204501 ◽  
Author(s):  
Devin Verreck ◽  
Anne S. Verhulst ◽  
Maarten L. Van de Put ◽  
Bart Sorée ◽  
Wim Magnus ◽  
...  
Keyword(s):  
Boundary Conditions ◽  
Envelope Function ◽  
Self Consistent ◽  
Transmitting Boundary

scholarly journals New perspectives for photoelectric phenomena

2016 ◽  
Vol 55 (4) ◽  
Author(s):  
Igor Lashkevych ◽  
Oleg Yu. Titov ◽  
Yuri G. Gurevich
Keyword(s):  
Solar Cells ◽  
Boundary Conditions ◽  
Maxwell’S Equations ◽  
Maxwell's Equations ◽  
Transport Phenomena ◽  
Space Charges ◽  
Recombination Processes ◽  
New Formulation ◽  
Physical Phenomena

The functioning of the solar cells (and photoelectric phenomena in general) relies on the photo-generation of carriers in p–n junctions and their subsequent recombination in the quasi-neutral regions. A number of basic issues concerning the physics of the operation of solar cells still remain obscure. This paper reports on some unsolved basic problems, namely: a model of the recombination processes that does not contradict Maxwell’s equations; boundary conditions; the role played by space charges in the transport phenomena, and the formation of quasi-neutral regions under the presence of nonequilibrium photo-generated carriers. In this work, a new formulation of the theory that explains the underlying physical phenomena involved in the generation of a photo-e.m.f. is presented.

scholarly journals Extension of the Chebyshev Method of Quassi-Linear Parabolic P.D.E.S With Mixed Boundary Conditions

2009 ◽  
Vol 6 (3) ◽  
pp. 603-611
Author(s):  
Baghdad Science Journal
Keyword(s):  
Error Analysis ◽  
Boundary Conditions ◽  
Numerical Solution ◽  
Linear Problem ◽  
Mixed Boundary ◽  
Mixed Boundary Conditions ◽  
Numerical Examples ◽  
Chebyshev Method

The researcher [1-10] proposed a method for computing the numerical solution to quasi-linear parabolic p.d.e.s using a Chebyshev method. The purpose of this paper is to extend the method to problems with mixed boundary conditions. An error analysis for the linear problem is given and a global element Chebyshev method is described. A comparison of various chebyshev methods is made by applying them to two-point eigenproblems. It is shown by analysis and numerical examples that the approach used to derive the generalized Chebyshev method is comparable, in terms of the accuracy obtained, with existing Chebyshev methods.

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