Numerical Solution of Elliptic Problems.

1987 ◽  
Vol 48 (178) ◽  
pp. 830
Author(s):  
Eugene L. Wachspress ◽  
Garrett Birkhoff ◽  
Robert E. Lynch
Keyword(s):  
Numerical Solution ◽  
Elliptic Problems

scholarly journals Numerical Solution of Fractional Elliptic Problems with Inhomogeneous Boundary Conditions

2021 ◽  
Vol 5 (3) ◽  
pp. 75
Author(s):  
Gábor Maros ◽  
Ferenc Izsák
Keyword(s):  
Numerical Solution ◽  
Fractional Order ◽  
Boundary Integral Equations ◽  
Real Life ◽  
Elliptic Problems ◽  
Boundary Integral ◽  
Laplacian Operator ◽  
Element Approximation ◽  
Fractional Laplacian Operator ◽  
Continuous Problem

The numerical solution of fractional-order elliptic problems is investigated in bounded domains. According to real-life situations, we assumed inhomogeneous boundary terms, while the underlying equations contain the full-space fractional Laplacian operator. The basis of the convergence analysis for a lower-order boundary element approximation is the theory for the corresponding continuous problem. In particular, we need continuity results for Riesz potentials and the fractional-order extension of the theory for boundary integral equations with the Laplacian operator. Accordingly, the convergence is stated in fractional-order Sobolev norms. The results were confirmed in a numerical experiment.

Numerical Solution of Elliptic Problems

1984 ◽  
Author(s):  
Garrett Birkhoff ◽  
Robert E. Lynch
Keyword(s):  
Numerical Solution ◽  
Elliptic Problems
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