Error Analysis for an Ale Evolving Surface Finite Element Method
نویسندگان
چکیده
We consider an arbitrary-Lagrangian-Eulerian evolving surface finite element method for the numerical approximation of advection and diffusion of a conserved scalar quantity on a moving surface. We describe the method, prove optimal order error bounds and present numerical simulations that agree with the theoretical results.
منابع مشابه
The Effects of Newmark Method Parameters on Errors in Dynamic Extended Finite Element Method Using Response Surface Method
The Newmark method is an effective method for numerical time integration in dynamic problems. The results of Newmark method are function of its parameters (β, γ and ∆t). In this paper, a stationary mode I dynamic crack problem is coded in extended finite element method )XFEM( framework in Matlab software and results are verified with analytical solution. This paper focuses on effects of main pa...
متن کاملAn ALE ESFEM for solving PDEs on evolving surfaces
Numerical methods for approximating the solution of partial differential equations on evolving hypersurfaces using surface finite elements on evolving triangulated surfaces are presented. In the ALE ESFEM the vertices of the triangles evolve with a velocity which is normal to the hypersurface whilst having a tangential velocity which is arbitrary. This is in contrast to the original evolving su...
متن کاملDynamic Fracture Analysis Using an Uncoupled Arbitrary Lagrangian Eulerian Finite Element Formulation
This paper deals with the implementation of an efficient Arbitrary Lagrangian Eulerian (ALE) formulation for the three dimensional finite element modeling of mode I self-similar dynamic fracture process. Contrary to the remeshing technique, the presented algorithm can continuously advance the crack with the one mesh topology. The uncoupled approach is employed to treat the equations. So, each t...
متن کاملError Analysis of a Space-Time Finite Element Method for Solving PDEs on Evolving Surfaces
In this paper we present an error analysis of an Eulerian finite element method for solving parabolic partial differential equations (PDEs) posed on evolving hypersurfaces in Rd, d = 2, 3. The method employs discontinuous piecewise linear in time–continuous piecewise linear in space finite elements and is based on a space-time weak formulation of a surface PDE problem. Trial and test surface fi...
متن کاملNumerical Analysis and Scientific Computing Preprint Seria Error analysis of a space-time finite element method for solving PDEs on evolving surfaces
In this paper we present an error analysis of an Eulerian finite element method for solving parabolic partial differential equations posed on evolving hypersurfaces in Rd, d = 2, 3. The method employs discontinuous piecewise linear in time – continuous piecewise linear in space finite elements and is based on a space-time weak formulation of a surface PDE problem. Trial and test surface finite ...
متن کامل