## Parallel finite element splitting-up method for parabolic problems.(English)Zbl 0747.65084

The paper treats a method for solving parabolic problems using a splitting-up principle, i.e. the 2D-problem is first discretized in time, afterwards a 1D-subproblem, fixing $$y$$, is solved in $$x$$-direction. Moving back the information at the time level $$t_{i+1}$$ to the time level $$t_ i$$, another 1D-problem is solved in $$y$$-direction. The solution of the 1D-problem is accomplished by applying cubic $$B$$- splines.
With the help of semigroup theory the convergence of the method is proved. A few examples conclude the careful investigation, showing in addition that the use of parallel processors is possible.

### MSC:

 65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs 65Y05 Parallel numerical computation 65M20 Method of lines for initial value and initial-boundary value problems involving PDEs 65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs 35K15 Initial value problems for second-order parabolic equations
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### References:

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