A Priori Estimates for Mixed Finite Element Approximations of Second-Order Hyperbolic Equations with Absorbing Boundary Conditions

1996 ◽  
Vol 33 (2) ◽  
pp. 492-504 ◽  
Author(s):  
Lawrence C. Cowsar ◽  
Todd F. Dupont ◽  
Mary F. Wheeler
Keyword(s):  
Finite Element ◽  
Boundary Conditions ◽  
A Priori Estimates ◽  
Hyperbolic Equations ◽  
Mixed Finite Element ◽  
A Priori ◽  
Absorbing Boundary Conditions ◽  
Absorbing Boundary ◽  
Finite Element Approximations ◽  
Priori Estimates

scholarly journals ABSORBING BOUNDARY CONDITIONS FOR THE TWO-DIMENSIONAL SCHRÖDINGER EQUATION WITH AN EXTERIOR POTENTIAL PART I: CONSTRUCTION AND A PRIORI ESTIMATES

2012 ◽  
Vol 22 (10) ◽  
pp. 1250026 ◽  
Author(s):  
XAVIER ANTOINE ◽  
CHRISTOPHE BESSE ◽  
PAULINE KLEIN
Keyword(s):  
Schrödinger Equation ◽  
Boundary Conditions ◽  
Schrodinger Equation ◽  
A Priori Estimates ◽  
Pseudodifferential Operators ◽  
A Priori ◽  
Absorbing Boundary Conditions ◽  
Two Dimensional ◽  
Absorbing Boundary ◽  
Priori Estimates

The aim of this paper is to construct some classes of absorbing boundary conditions for the two-dimensional Schrödinger equation with a time and space varying exterior potential and for general convex smooth boundaries. The construction is based on asymptotics of the inhomogeneous pseudodifferential operators defining the related Dirichlet-to-Neumann operator. Furthermore, a priori estimates are developed for the truncated problems with various increasing order boundary conditions. The effective numerical approximation will be treated in a second paper.

scholarly journals A PROBLEM WITH DISPLACEMENTS IN THE BOUNDARY CONDITIONS

2017 ◽  
Vol 17 (8) ◽  
pp. 102-107
Author(s):  
E.A. Utkina
Keyword(s):  
Boundary Conditions ◽  
Unknown Function ◽  
A Priori Estimates ◽  
Hyperbolic Equations ◽  
A Priori ◽  
Fredholm Equations ◽  
Priori Estimates ◽  
Linear Hyperbolic Equations

A problem with conditions relating to the values of an unknown function on the opposite sides of a rectangular characteristiс domain D for a linear hyperbolic equations is considered. This problem is reduced to the system of Fredholm equations of the second kind. The proof of solvability is based on the a priori estimates of additional conditions on the coefficients of the equation.

scholarly journals Uniform a priori estimates for elliptic problems with impedance boundary conditions

2020 ◽  
Vol 19 (5) ◽  
pp. 2445-2471
Author(s):  
Théophile Chaumont-Frelet ◽  
◽  
Serge Nicaise ◽  
Jérôme Tomezyk ◽  
Keyword(s):  
Boundary Conditions ◽  
A Priori Estimates ◽  
A Priori ◽  
Elliptic Problems ◽  
Impedance Boundary ◽  
Impedance Boundary Conditions ◽  
Priori Estimates

scholarly journals On the solvability of parabolic and hyperbolic problems with a boundary integral condition

2002 ◽  
Vol 31 (4) ◽  
pp. 201-213 ◽  
Author(s):  
Abdelfatah Bouziani
Keyword(s):  
A Priori Estimates ◽  
Hyperbolic Equations ◽  
A Priori ◽  
Integral Condition ◽  
Generalized Solution ◽  
Boundary Integral ◽  
Analysis Method ◽  
Hyperbolic Problems ◽  
Priori Estimates ◽  
Abstract Formulation

We prove the existence, uniqueness, and the continuous dependence of a generalized solution upon the data of certain parabolic and hyperbolic equations with a boundary integral condition. The proof uses a functional analysis method based on a priori estimates established in nonclassical function spaces, and on the density of the range of the linear operator associated to the abstract formulation of the studied problem.

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