Journal of Scientific Computing

Abstract For the generalized eigenvalue problem, a quotient function is devised for estimating eigenvalues in terms of an approximate eigenvector. This gives rise to an infinite family of quotients, a disc centered at the Rayleigh quotient, all entirely arguable to be used in estimation. Although the Rayleigh quotient is among them, one can suggest using it only in an auxiliary manner to choose t…

Abstract In this paper, we develop an efficient Fourier-Legendre spectral-Galerkin method for solving elliptic partial differential equations on general two-dimensional domains. A key core of our approach is employing a harmonic map to handle the general physical domains. This technique ensures broad geometric applicability, making the method highly effective for both complex star-shaped and nons…

Abstract This paper presents an innovative continuous linear finite element approach to effectively solve biharmonic problems on surfaces. The key idea behind this method lies in the strategic utilization of a surface gradient recovery operator to compute the second-order surface derivative of a piecewise continuous linear function defined on the approximate surface, as conventional notions of se…