New expansions of numerical eigenvalues for -Δu = λρu by nonconforming elements

The paper explores new expansions of the eigenvalues for -Δu = Λpu in S with Dirichlet boundary conditions by the bilinear element (denoted Q 1 ) and three nonconforming elements, the rotated bilinear element (denoted Q 1 rot ), the extension of Q 1 rot (denoted EQ 1 rot ) and Wilson's elements. The expansions indicate that Q 1 and Q 1 rot provide upper bounds of the eigenvalues, and that EQ 1 rot and Wilson's elements provide lower bounds of the eigenvalues. By extrapolation, the O(h 4 ) convergence rate can be obtained, where h is the maximal boundary length of uniform rectangles. Numerical experiments are carried out to verify the theoretical analysis made.

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