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In this talk, I begin with a review of different geometric flows (PDEs) including mean curvature (curve shortening) flow,surface diffusion flow, Willmore flow, etc., which arise from materials science...
An unfitted interface penalty finite element method is proposed for the interface problems, in which Nitsche's method together with the ideas of merging elements and harmonic weighing fluxes are used,...
In this talk, we present numerical approximations of a phase-field model for two-phase ferrofluids, which consists of the Navier-Stokes equations, the Cahn-Hilliard equation, the magnetostatic equatio...
We present a mixednite element method for a model of the flow in a Hele-Shaw cell of 2-D fluid droplets surrounded by air driven by surface tension and actuated by an electric &...
Based on H1-Galerkin mixed finite element method with nonconforming quasi-Wilson element, a numerical approximate scheme is established for pseudo-hyperbolic equations under arbitrary quadrilateral me...
In an earlier paper, we presented an iterative algorithm for reconstructing a three dimensional density function from a set of two dimensional electron microscopy images. By minimizing an energy fun...
In this paper, we present a novel L2-gradient flow based semi-implicit finite element method for solving a variational model of image reconstruction under various data scenarios, especially for the ...
We propose a condition under which the heterogeneous multiscale ite element method converges for elliptic problem with nonsmooth coe眂ients, and obtain the optimal convergence rate for elliptic prob...
An integro-differential equation of hyperbolic type, with mixed boundary conditions, is considered. A continuous space-time finite element method of degree one is formulated. A posteriori error repres...
The objectives of this study are to model the endocardiac radiofrequency (RF) ablation procedure and to employ the Hyperbolic Bioheat Equation (HBE), which takes the thermal wave behaviour into accoun...
Abstract: In this paper, the linear free flexural vibration of cracked functionally graded material plates is studied using the extended finite element method. A 4-noded quadrilateral plate bending el...
Abstract: This letter aims at resolving the issues raised in the recent short communication [1] and answered by [2] by proposing a systematic approximation scheme based on non-mapped shape functions, ...
An interface stabilised finite element method for the incompressible Navier-Stokes equations is presented. The method inherits the attractive stabilising mechanism of upwinded discon-tinuous Galerkin...
We continue our study on variable order Arnold-Falk-Winther elements for 2D elasticity in context of both affine and parametric curvilinear elements. We present an $h$-stability result for affine ele...
Abstract. In this paper, we analyze the convergence of the adaptive conforming P 1 element method with the red-green refinement. Since the mesh after refining is not nested into the one before, the Ga...

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