Boundedness and continuity of solutions to linearelliptic boundary value problems in two dimensions

1994 ◽  
Vol 298 (1) ◽  
pp. 719-727 ◽  
Author(s):  
Konrad Gr�ger
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Two Dimensions ◽  
Continuity Of Solutions

scholarly journals A New Formulation for Solutions of Boundary Value Problems Using Domain-type Approximations and Local Integral Equations

2007 ◽  
Vol 1 (2) ◽  
Author(s):  
V. Sladek ◽  
J. Sladek
Keyword(s):  
Boundary Value Problems ◽  
Boundary Value ◽  
Two Dimensions ◽  
Boundary Integral ◽  
Primary Field ◽  
Type Approximation ◽  
Domain Type ◽  
Local Integral ◽  
New Formulation ◽  
Local Integral Equations

The boundary and domain-type approximations are discussed in boundary integral equation formulations for solution of boundary value problems. A new approach is proposed with using a domain-type approximation of the primary field and collocation of boundary conditions at boundary nodes and local integral representation of the primary field at interior nodes. Two kinds of the domain-type approximation are utilized. The proposed method is illustrated on potential problems in two dimensions.

A NEW BACKUS–GILBERT MESHLESS APPROXIMATION METHOD FOR INITIAL-BOUNDARY VALUE PARTIAL DIFFERENTIAL EQUATIONS

2006 ◽  
Vol 03 (03) ◽  
pp. 337-353 ◽  
Author(s):  
CHRISTOPHER D. BLAKELY
Keyword(s):  
Boundary Value Problems ◽  
Approximation Method ◽  
Burgers Equation ◽  
Boundary Value ◽  
Initial Boundary ◽  
Two Dimensions ◽  
Initial Boundary Value Problems ◽  
Meshless Collocation ◽  
Meshless Approximation ◽  
Initial Boundary Value

A Backus–Gilbert approximation method is introduced in this paper as a tool for numerically solving initial-boundary value problems. The formulation of the method with its connection to the standard moving least-squares formulation will be given along with some numerical examples including a numerical solution to the viscous nonlinear Burgers equation in two-dimensions. In addition, we highlight some of the main advantages of the method over previous numerical methods based on meshless collocation approximation in order to validate its robust approximating power and easy handling of initial-boundary value problems.

scholarly journals Green's Functions for Mixed Boundary Value Problems in Regions of Irregular Shape

2007 ◽  
Vol 4 (3) ◽  
Author(s):  
Yuri A. Melnikov ◽  
Max Y. Melnikov
Keyword(s):  
Boundary Value Problems ◽  
Green's Functions ◽  
Green’S Functions ◽  
Mixed Boundary ◽  
Boundary Value ◽  
Two Dimensions ◽  
Mixed Boundary Value Problems ◽  
Different Types ◽  
Multiply Connected Regions ◽  
Klein Gordon

A semi-analytic approach is applied to the construction of Green's functions and matrices of Green's type for Laplace and Klein-Gordon equation in two dimensions. Mixed boundary value problems posed on multiply connected regions are considered. Statements of the problems are complicated by intricate geometry of the regions and different types of boundary conditions imposed on different fragments of the boundary. The approach is based on a combination of the Green's function method and the method of functional equations. Kernels of resolving potentials representing the regular components of the Green's functions to be constructed are built with Green's functions obtained for regions of standard shape.

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