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Keywords
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anisotropic sobolev space
Boundary Integral Method
Heat Equation
Initial Boundary Value Problem
Operator Equation
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(2)
Boundary integral operators for the heat equation
The Single Layer Heat Potential and Galerkin Boundary Element Methods for the Heat Equation
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COERCIVITY OF THE SINGLE LAYER HEAT POTENTIAL
COERCIVITY OF THE SINGLE LAYER HEAT POTENTIAL,International Journal of Computer Mathematics,Douglas N. Arnold,Patrick J. Noon
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COERCIVITY OF THE SINGLE LAYER HEAT POTENTIAL
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Citations: 11
)
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Douglas N. Arnold
,
Patrick J. Noon
The single layer heat potential operator,K, arises in the solution of initial boundary value problems for the
heat equation
using boundary integral methods. In this note we show thatK maps a certain
anisotropic Sobolev space
isomorphically onto its dual, and, moreover, satises the coercivity inequality hKq;qi ckqk 2 . We thereby establish the well posedness of the
operator equation
Kq = f and provide a basis for the analysis of the discretizations.
Journal:
International Journal of Computer Mathematics  IJCM
Cumulative
Annual
Citation Context
(10)
...Sobolev space [
1
, 3]. Likewise, the thermal double layer operator is compact in the proper setting [3, 5]. This result is the background for the analysis of the Galerkin method in both space and time...
Johannes Tausch
.
Nyström discretization of parabolic boundary integral equations
...These results extend now the standard variational techniques for steadystate strongly elliptic boundary integral equations as in [3] and [8] to the unsteady viscous compressible flow case, by employing the tools due as in [
1
], [2] and [7] for the heat equations...
...We now extend to the equation (3.1) those approaches in [
1
], [2] and [7] for treating heat equation...
FriedrichKarl Hebeker
,
et al.
An InitialBoundary Value Problem for the Viscous Compressible Flow
...The boundary integral solution of parabolic initialboundary value problems can be, and has been, applied also for more general domains covering even the case of Lipschitz domains [
1
],[5],[6],[10],[11],[14],[20]...
...550 M. Costabel, J. Saranen approximation in [
1
],[6],[17]...
...The operator V satisfies all the assumptions (2.1ah), see [8],[9] and also [
1
],[6],[13] and [17]...
M. Costabel
,
et al.
The spline collocation method for parabolic boundary integral equation...
...For the basic parabolic boundary integral operators (single layer and the hypersingular operator), we thus recover the result of [15], [
2
], [4], [9]...
M. Costabel
,
et al.
Parabolic boundary integral operators symbolic representation and basi...
...The operator L satisfies all the assumptions (2.1ah), see [
2
, 8, 16, 24]...
...The first expression on the right hand side is easily seen to be negative for 2 [ 2;0] and the second for 2 [0;
2
]...
M. Costabel
,
et al.
Spline collocation for convolutional parabolic boundary integral equat...
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Citations: 1
)
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Citations
(11)
Nyström discretization of parabolic boundary integral equations
Johannes Tausch
Journal:
Applied Numerical Mathematics  APPL NUMER MATH
, vol. 59, no. 11, pp. 28432856, 2009
An InitialBoundary Value Problem for the Viscous Compressible Flow
FriedrichKarl Hebeker
,
George C. Hsiao
Published in 2007.
An efficient and fast parallel method for Volterra integral equations of Abel type
(
Citations: 3
)
Giovanni Capobianco
,
Dajana Conte
Journal:
Journal of Computational and Applied Mathematics  J COMPUT APPL MATH
, vol. 189, no. 1, pp. 481493, 2006
The spline collocation method for parabolic boundary integral equations on smooth curves
M. Costabel
,
J. Saranen
Journal:
Numerische Mathematik  NUMER MATH
, vol. 93, no. 3, pp. 549562, 2003
Parabolic boundary integral operators symbolic representation and basic properties
(
Citations: 7
)
M. Costabel
,
J. Saranen
Journal:
Integral Equations and Operator Theory  INTEGRAL EQUATION OPER THEORY
, vol. 40, no. 2, pp. 185211, 2001