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.


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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