A Mixed Finite Element Method for EWOD That Directly Computes the Position of the Moving Interface | Zendy

Richard S. Falk | Zendy; Shawn W. Walker | Zendy

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A Mixed Finite Element Method for EWOD That Directly Computes the Position of the Moving Interface

Author(s) -

Richard S. Falk,

Shawn W. Walker

Publication year - 2013

Publication title -

siam journal on numerical analysis

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 2.78

H-Index - 134

eISSN - 1095-7170

pISSN - 0036-1429

DOI - 10.1137/12088567x

Subject(s) - finite element method , mathematics , curvature , microscale chemistry , robustness (evolution) , mathematical analysis , position (finance) , mixed finite element method , geometry , physics , biochemistry , chemistry , mathematics education , gene , finance , economics , thermodynamics

. A new mixed finite element method is proposed and analyzed for simulating twophase droplet motion in a microscale device driven by electrowetting-on-dielectric. The new feature of the method is that the finite element scheme is based on a weak formulation of the problem which includes the position of the moving interface and the curvature of its boundary as basic unknowns to be determined along with the velocity field and pressure. Well-posedness of the semidiscrete and fully discrete formulations and error estimates with minimal regularity assumptions are proved. Numerical examples are given to illustrate the robustness of the method. Key words. two-phase flow Hele-Shaw flow, front-tracking, mixed finite element method, surface tension, AMS subject classifications. 65N30, 76T10 DOI. 10.1137/12088567

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