Convergence of the Projection-Difference Method for the Approximate Solution of a Smoothly Solvable Parabolic Equation with a Weighted Integral Condition

We search for an approximate solution of an abstract linear parabolic equation in a Hilbert space with a nonlocal weighted integral condition by the projection-difference method and the implicit Euler method in time. The approximation of the problem with respect to spatial variables is oriented to t...

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Published inJournal of mathematical sciences (New York, N.Y.) Vol. 275; no. 5; pp. 583 - 591
Main Author Petrova, A. A.
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 01.10.2023
Springer
Springer Nature B.V
Subjects
Convergence
Exact solutions
Finite element method
Hilbert space
Mathematics
Mathematics and Statistics
Smoothness
Subspaces
nonlocal weighted integral condition
Hilbert space
parabolic equation
implicit Euler method
35K90
projection-difference method
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ISSN1072-3374
1573-8795
DOI10.1007/s10958-023-06699-1

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Summary:We search for an approximate solution of an abstract linear parabolic equation in a Hilbert space with a nonlocal weighted integral condition by the projection-difference method and the implicit Euler method in time. The approximation of the problem with respect to spatial variables is oriented to the finite element method in the case of arbitrary projection subspaces under an additional smoothness condition. Estimates of errors of approximate solutions are established, the convergence of approximate solutions to the exact solution is proved, and the convergence rate is estimated.
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ISSN:1072-3374
1573-8795
DOI:10.1007/s10958-023-06699-1