Title of article :
Some error estimates on the finite element approximation for two-dimensional elliptic problem with nonlocal boundary
Author/Authors :
Nie، نويسنده , , Cunyun and Yu، نويسنده , , Haiyuan، نويسنده ,
Issue Information :
روزنامه با شماره پیاپی سال 2013
Pages :
8
From page :
31
To page :
38
Abstract :
We construct a linear finite element scheme for the two-dimensional elliptic problem with nonlocal boundary conditions. In order to obtain the optimal error estimates in the L 2 norm, we innovatively decompose the original elliptic problem into two subproblems by the principle of superposition for the differential equation: nonhomogeneous one with Dirichlet boundary and homogeneous one with nonlocal boundary. Then, we prove that our approximate solution has saturated convergent order by properly introducing a projection operator and the maximum principle. In addition, we design an attractive preconditioning algorithm for our discrete system, which improves the efficiency of our computation. Finally, numerical experiments verify our theoretical results.
Keywords :
error estimates , A preconditioning algorithm , Two dimension elliptic problem , Linear finite element , Nonlocal boundary conditions
Journal title :
Applied Numerical Mathematics
Serial Year :
2013
Journal title :
Applied Numerical Mathematics
Record number :
1529791
Link To Document :
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