TY - JOUR
T1 - Numerical verifications for solutions to elliptic equations using residual iterations with a higher order finite element
AU - Yamamoto, Nobito
AU - Nakao, Mitsuhiro T.
PY - 1995/6/20
Y1 - 1995/6/20
N2 - The verifications of solutions to weakly nonlinear elliptic equations by the method described e.g. by Nakao (1988, 1989), etc. are sometimes hardly accomplished when the right-hand sides of the equations are very large. To overcome such difficulties, a residual iteration technique with approximate solution was introduced by Nakao (1993). In the present paper, we propose an a posteriori method for the residual iteration, and show that a remarkable improvement in efficiency and in accuracy of the verification can be obtained when we use a higher order finite element.
AB - The verifications of solutions to weakly nonlinear elliptic equations by the method described e.g. by Nakao (1988, 1989), etc. are sometimes hardly accomplished when the right-hand sides of the equations are very large. To overcome such difficulties, a residual iteration technique with approximate solution was introduced by Nakao (1993). In the present paper, we propose an a posteriori method for the residual iteration, and show that a remarkable improvement in efficiency and in accuracy of the verification can be obtained when we use a higher order finite element.
KW - Nonlinear elliptic problem
KW - Numerical verification
KW - Residual iteration
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U2 - 10.1016/0377-0427(94)00096-J
DO - 10.1016/0377-0427(94)00096-J
M3 - Article
AN - SCOPUS:0000566179
VL - 60
SP - 271
EP - 279
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
SN - 0377-0427
IS - 1-2
ER -