Details
| Original language | English |
|---|---|
| Pages (from-to) | 301-317 |
| Number of pages | 17 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 92 |
| Issue number | 3 |
| Publication status | Published - 19 Oct 2012 |
Abstract
Numerical schemes for the approximative solution of advection-diffusion-reaction equations are often flawed because of spurious oscillations, caused by steep gradients or dominant advection or reaction. In addition, for strong coupled nonlinear processes, which may be described by a set of hyperbolic PDEs, established time stepping schemes lack either accuracy or stability to provide a reliable solution. In this contribution, an advanced numerical scheme for this class of problems is suggested by combining sophisticated stabilization techniques, namely the finite calculus (FIC-FEM) scheme introduced by Oñate etal. with time-discontinuous Galerkin (TDG) methods. Whereas the former one provides a stabilization technique for the numerical treatment of steep gradients for advection-dominated problems, the latter ensures reliable solutions with regard to the temporal evolution. A brief theoretical outline on the superior behavior of both approaches will be presented and underlined with related computational tests. The performance of the suggested FIC-TDG finite element approach will be discussed exemplarily on a bioregulatory model for bone fracture healing proposed by Geris et al., which consists of at least 12 coupled hyperbolic evolution equations.
Keywords
- Advection, Bone fracture healing, Diffusion, Finite calculus, Finite element, Hyperbolic PDE, Reaction, Time-discontinuous Galerkin
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Engineering(all)
- General Engineering
- Mathematics(all)
- Applied Mathematics
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In: International Journal for Numerical Methods in Engineering, Vol. 92, No. 3, 19.10.2012, p. 301-317.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - A combined FIC-TDG finite element approach for the numerical solution of coupled advection-diffusion-reaction equations with application to a bioregulatory model for bone fracture healing
AU - Sapotnick, A.
AU - Nackenhorst, U.
PY - 2012/10/19
Y1 - 2012/10/19
N2 - Numerical schemes for the approximative solution of advection-diffusion-reaction equations are often flawed because of spurious oscillations, caused by steep gradients or dominant advection or reaction. In addition, for strong coupled nonlinear processes, which may be described by a set of hyperbolic PDEs, established time stepping schemes lack either accuracy or stability to provide a reliable solution. In this contribution, an advanced numerical scheme for this class of problems is suggested by combining sophisticated stabilization techniques, namely the finite calculus (FIC-FEM) scheme introduced by Oñate etal. with time-discontinuous Galerkin (TDG) methods. Whereas the former one provides a stabilization technique for the numerical treatment of steep gradients for advection-dominated problems, the latter ensures reliable solutions with regard to the temporal evolution. A brief theoretical outline on the superior behavior of both approaches will be presented and underlined with related computational tests. The performance of the suggested FIC-TDG finite element approach will be discussed exemplarily on a bioregulatory model for bone fracture healing proposed by Geris et al., which consists of at least 12 coupled hyperbolic evolution equations.
AB - Numerical schemes for the approximative solution of advection-diffusion-reaction equations are often flawed because of spurious oscillations, caused by steep gradients or dominant advection or reaction. In addition, for strong coupled nonlinear processes, which may be described by a set of hyperbolic PDEs, established time stepping schemes lack either accuracy or stability to provide a reliable solution. In this contribution, an advanced numerical scheme for this class of problems is suggested by combining sophisticated stabilization techniques, namely the finite calculus (FIC-FEM) scheme introduced by Oñate etal. with time-discontinuous Galerkin (TDG) methods. Whereas the former one provides a stabilization technique for the numerical treatment of steep gradients for advection-dominated problems, the latter ensures reliable solutions with regard to the temporal evolution. A brief theoretical outline on the superior behavior of both approaches will be presented and underlined with related computational tests. The performance of the suggested FIC-TDG finite element approach will be discussed exemplarily on a bioregulatory model for bone fracture healing proposed by Geris et al., which consists of at least 12 coupled hyperbolic evolution equations.
KW - Advection
KW - Bone fracture healing
KW - Diffusion
KW - Finite calculus
KW - Finite element
KW - Hyperbolic PDE
KW - Reaction
KW - Time-discontinuous Galerkin
UR - http://www.scopus.com/inward/record.url?scp=84866849546&partnerID=8YFLogxK
U2 - 10.1002/nme.4338
DO - 10.1002/nme.4338
M3 - Article
AN - SCOPUS:84866849546
VL - 92
SP - 301
EP - 317
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 3
ER -