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- W254959322 abstract "A semilinear elliptic boundary value problem of the form + g{xyVi..,) = 0 and a cor responding discrete problem based on the finite element method are considered. The method of alternative problems is used to reduce the boundary value problem to an equivalent finitedimensional problem B{c, A) = 0. The bifurcation function B(c, A) is a vector field on for fixed A. The solutions of the reduced problem are in a one-to-one correspondence with the solutions of the boundary value problem. The method of alternative problems is also applied to reduce the discrete problem to an equivalent lower-dimensional problem. An approximate bifurcation function Ba,(c, A) for the lower-dimensional problem is also defined as a vector field on whose zeros are in a one-to-one correspondence with the solutions of the discrete prob lem. Estimates of the differences 5(c, A) A), Bc(c, A) — (BA)c(e, A), and £{Cy A) —£a(c. A) are derived. Here, 5(c, A) (resp. Sa(c,A)) denotes the value of energy functional associated with the boundary value problem (resp. the discrete problem). Morse decompositions are computed for some classical examples, and their bifurcation diagrams are presented. Results &om numerical experiments on the orders of convergence for the difference B(c, A) — A) are presented." @default.
- W254959322 created "2016-06-24" @default.
- W254959322 creator A5006939410 @default.
- W254959322 date "2018-08-13" @default.
- W254959322 modified "2023-09-23" @default.
- W254959322 title "Error estimates for the bifurcation function for semilinear elliptic boundary value problems" @default.
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- W254959322 doi "https://doi.org/10.31274/rtd-180813-13919" @default.
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