Piecewise linear approach to the stokes equations in 3-D

• Published in: Applied mathematics and computation Vol. 72; no. 1; pp. 61 - 75
• Main Author: Chang, Ching Lung
• Format: Journal Article
• Language: English
• Published: New York, NY Elsevier Inc 15.09.1995; Elsevier
• Subjects: Classical and quantum physics: mechanics and fields; Classical mechanics of continuous media: general mathematical aspects; Computational methods in fluid dynamics; Exact sciences and technology; Fluid dynamics; Fluid mechanics: general mathematical aspects; Fundamental areas of phenomenology (including applications); Mathematical methods in physics; Mathematics; Numerical analysis; Numerical analysis. Scientific computation; Numerical approximation and analysis; Ordinary and partial differential equations, boundary value problems; Partial differential equations, boundary value problems; Physics; Sciences and techniques of general use; Finite element method; Interpolation; Three dimensional model; Least squares approximations; Fluid dynamics; Partial differential equations; Stokes problem; Convergence rate; Incompressible fluid; Mixed method; Equation system
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/0096-3003(94)00176-5

Since the beginning of the 1970's, people have developed mixed finite element methods for incompressible flow. The velocity and pressure interpolations are required to satisfy a Ladyshenskaya-Babuska-Brezzi (LBB) condition which precludes many natural elements. Over the past 20 years, most mathematicians and engineers believed this to be necessary. In this research, a least-squares method for three-dimensional (3-D) problems is proposed. This method leads to a minimization problem and thus it is not subject to the restriction of the LBB condition. Piecewise linear elements can be applied for the approximation functions; the simplest and natural elements are easy to program and achieve optimal rates of convergence.