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Conforming spectral approximations for non-conforming domain decompositions. (English) Zbl 0943.65149

Summary: A spectral domain decomposition scheme is introduced for the numerical solution of second- and fourth-order elliptic problems. The technique is applicable to certain domain decompositions of rectangular or rectangularly decomposable domains. It is shown that it yields approximations which are pointwise \(C^0\) continuous across the subdomain interfaces for second-order problems and pointwise \(C^1\) continuous across the subdomain interfaces for fourth-order problems.

MSC:

65N55 Multigrid methods; domain decomposition for boundary value problems involving PDEs
65N35 Spectral, collocation and related methods for boundary value problems involving PDEs
35J25 Boundary value problems for second-order elliptic equations
35J40 Boundary value problems for higher-order elliptic equations
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References:

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