A spectral mimetic least-squares method

A spectral mimetic least-squares method for the Stokes equations with no-slip boundary condition

Formulation of locally conservative least-squares finite element methods (LSFEM) for the Stokes equations with the no-slip boundary condition has been a long standing problem. Existing LSFEMs that yield exactly divergence free velocities require nonstandard boundary conditions [3], while methods that admit the no-slip condition satisfy the incompressibility equation only approximately [4, Chapt...

Rehabilitation of the Lowest-Order Raviart-Thomas Element on Quadrilateral Grids

A recent study [4] reveals that convergence of finite element methods usingH(div ,Ω)compatible finite element spaces deteriorates on non-affine quadrilateral grids. This phenomena is particularly troublesome for the lowest-order Raviart-Thomas elements, because it implies loss of convergence in some norms for finite element solutions of mixed and least-squares methods. In this paper we propose ...

Least Squares Techniques for Extracting Water Level Fluctuations in the Persian Gulf and Oman Sea

Extracting the main cyclic fluctuations from sea level changes of the Persian Gulf and Oman Sea is vital for understanding the behavior of tides and isolating non-tidal impacts such as those related to climate and changes in the ocean-sea circulations. This study compares two spectral analysis methods including: Least Squares Spectral Analysis (LSSA) and Least Squares Harmonic Estimation (LSHE)...

A Least Squares Spectral Element Method for Incompressible Flow Simulations

Chebyshev Weighted Norm Least - Squares Spectral Methods for the Elliptic Problem

We develop and analyze a first-order system least-squares spectral method for the second-order elliptic boundary value problem with variable coefficients. We first analyze the Chebyshev weighted norm least-squares functional defined by the sum of the Lwand H−1 w norm of the residual equations and then we replace the negative norm by the discrete negative norm and analyze the discrete Chebyshev ...