<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si12.gif" overflow="scroll"><mml:mtext>P2Q2Iso2D=2D</mml:mtext></mml:math> Isoparametric FEM in Matlab

Bartels, Sören; Carstensen, Carsten; Hecht, A

doi:10.1016/j.cam.2005.04.032

Cited by 9 publications

(3 citation statements)

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“…To this end, we use the notation \widehat \scrT to indicate a mesh consisting of piecewise affine elements (not curved), where \widehat T \in \widehat \scrT indicates a specific affine element. Moreover, we write \widehat \Omega = int \bigl( \cup [13]. This gives a partition of the true domain \Omega s into a mesh of nonlinear elements \scrT s = \{ T s \} .…”

Section: Fe Spacesmentioning

confidence: 99%

“…Ts for some T s \in \scrT s , \eta \in \scrP (T ref )\} . However, this is not always practical, so we take an FE (Lagrange) approach to the local charts (e.g., iso-parametric [13]). Define the FE space (6) G k ( \widehat…”

Section: Fe Spacesmentioning

confidence: 99%

“…We consider a problem of droplet motion in microfluidics applications driven by electro-wetting-on-dielectric (EWOD) [22,40,55]. The model is essentially Hele--Shaw flow with surface tension and electric effects [56,54]: \alpha \partial t u + \beta u + \nabla p = 0, \nabla \cdot u = 0 in \Omega (t), p = \kappa (t) + E(t), \partial t x \cdot n = u \cdot n on \Gamma (t) \equiv \partial\Omega (t), (13) where \Omega (t) \subset \BbbR 2 is the time-dependent droplet domain, \Gamma (t) \equiv \partial\Omega (t) is the liquid-gas interface (a closed one dimensional curve), u is the fluid velocity, p is the pressure, \kappa (t) is the signed curvature of \Gamma (t), E(t) is the electro-wetting force, n(t) is the outer unit normal vector of \Gamma (t), and x(t) is the parameterization of \Gamma (t); hence, this is a moving interface problem. The constants \alpha , \beta are material parameters.…”

Section: Example: Ewodmentioning

confidence: 99%

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FELICITY: A Matlab/C++ Toolbox for Developing Finite Element Methods and Simulation Modeling

Walker¹

2018

SIAM J. Sci. Comput.

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\bfA \bfb \bfs \bft \bfr \bfa \bfc \bft. This paper describes a MATLAB/C++ finite element toolbox, called FELICITY, for simulating various types of systems of partial differential equations (e.g., coupled elliptic/parabolic problems) using the finite element method. It uses MATLAB in an object-oriented way for high-level manipulation of data structures in finite element codes, while utilizing a domain-specific language (DSL) and code generation to automate low-level tasks such as matrix assembly (via the MATLAB mex interface). We describe the fundamental functionality of the toolbox's MATLAB interface, such as using higher order Lagrange (simplicial) meshes, defining finite element spaces, allocating degreesof-freedom, assembling discrete bilinear and linear forms, and interpolation over meshes. Moreover, we describe in-depth how automatic code generation is implemented in FELICITY. Two example problems and their implementation are provided to demonstrate the ability of FELICITY to solve coupled problems with interacting subdomains of different co-dimension. Future improvements are also discussed. \bfK \bfe \bfy \bfw \bfo \bfr \bfd \bfs. finite elements, coupled systems, geometric flows, code generation, MATLAB, open source software \bfA \bfM \bfS \bfs \bfu \bfb \bfj \bfe \bfc \bft \bfc \bfl \bfa \bfs \bfs \bfi fi\bfc \bfa \bft \bfi \bfo \bfn \bfs .

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Section: Fe Spacesmentioning

confidence: 99%

Section: Fe Spacesmentioning

confidence: 99%

Section: Example: Ewodmentioning

confidence: 99%

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FELICITY: A Matlab/C++ Toolbox for Developing Finite Element Methods and Simulation Modeling

Walker¹

2018

SIAM J. Sci. Comput.

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A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method

Abdulle

Nonnenmacher

2013

Numerical Methods Partial

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We present an a posteriori error analysis in quantities of interest for elliptic homogenization problems discretized by the finite element heterogeneous multiscale method. The multiscale method is based on a macro-to-micro formulation, where the macroscopic physical problem is discretized in a macroscopic finite element space and the missing macroscopic data is recovered on-the-fly using the solutions of corresponding microscopic problems. We propose a new framework that allows to follow the concept of the (single-scale) dual-weighted residual method at the macroscopic level in order to derive a posteriori error estimates in quantities of interests for multiscale problems. Local error indicators, derived in the macroscopic domain, can be used for adaptive goal-oriented mesh refinement. These error indicators rely only on available macroscopic and microscopic solutions. We further provide a detailed analysis of the data approximation error, including the quadrature errors. Numerical experiments confirm the efficiency of the adaptive method and the effectivity of our error estimates in the quantities of interest.

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Monotone Multigrid Methods Based on Parametric Finite Elements

Dickopf

Krause

2013

Lecture Notes in Computational Science and Engineering

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P2Q2Iso2D=2D Isoparametric FEM in Matlab

Cited by 9 publications

References 5 publications

FELICITY: A Matlab/C++ Toolbox for Developing Finite Element Methods and Simulation Modeling

FELICITY: A Matlab/C++ Toolbox for Developing Finite Element Methods and Simulation Modeling

A posteriori error estimates in quantities of interest for the finite element heterogeneous multiscale method

Monotone Multigrid Methods Based on Parametric Finite Elements

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