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math.NA2022
Projection error-based guaranteed L2 error bounds for finite element approximations of Laplace eigenfunctions
Xuefeng Liu, Tomáš Vejchodský
For conforming finite element approximations of the Laplacian eigenfunctions, a fully computable guaranteed error bound in the norm sense is proposed. The bound is based on t…
math.NA2022
Shape optimization for the Laplacian eigenvalue over triangles and its application to interpolation error constant estimation
Ryoki Endo, Xuefeng Liu
A computer-assisted proof is proposed for the Laplacian eigenvalue minimization problems over triangular domains under diameter constraints. The proof utilizes recently developed g…