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By improving the trace finite element method, we developed another higher-order trace finite element method by integrating on the surface with exact geometry description. This method restricts the finite element space on the volume mesh to the surface accurately, and approximates Laplace-Beltrami operator on the surface by calculating the high-order numerical integration on the exact surface directly. We employ this method to calculate the Laplace-Beltrami equation and the Laplace-Beltrami eigenvalue problem. Numerical error analysis shows that this method has an optimal convergence order in both problems. Numerical experiments verify the correctness of the theoretical analysis. The algorithm is more accurate and easier to implement than the existing high-order trace finite element method.
This paper studies a model of two-phase flow with an immersed material viscous interface and a finite element method for numerical solution of the resulting system of PDEs. The interaction between the bulk and surface media is characterized by no-pen
We propose an energy-stable parametric finite element method (ES-PFEM) to discretize the motion of a closed curve under surface diffusion with an anisotropic surface energy $gamma(theta)$ -- anisotropic surface diffusion -- in two dimensions, while $
In this paper we consider the Virtual Element discretization of a minimal surface problem, a quasi-linear elliptic partial differential equation modeling the problem of minimizing the area of a surface subject to a prescribed boundary condition. We d
Fourth-order differential equations play an important role in many applications in science and engineering. In this paper, we present a three-field mixed finite-element formulation for fourth-order problems, with a focus on the effective treatment of
This paper constructs and analyzes a boundary correction finite element method for the Stokes problem based on the Scott-Vogelius pair on Clough-Tocher splits. The velocity space consists of continuous piecewise quadratic polynomials, and the pressur