Details
| Original language | English |
|---|---|
| Pages (from-to) | A681-A710 |
| Journal | SIAM Journal on Scientific Computing |
| Volume | 39 |
| Issue number | 3 |
| Publication status | Published - 2017 |
| Externally published | Yes |
Abstract
In this paper, we consider numerical methods for nonlinear diffusion problems where the diffusion term follows a power law, e.g., p-Laplace-type problems. In the first part, we present continuous higher order finite element discretizations for the model problem and we derive error estimates. In the second part, we discuss Newton iterative methods based on residual-based linesearch and error-oriented globalization, which are employed for the numerical solution of the produced nonlinear algebraic system. Third, we formulate the original problem as a saddle point problem in the frame of augmented Lagrangian techniques and present two iterative methods for its solution. We conduct a systematic investigation of all solution algorithms. These algorithms are compared with respect to computational cost and their efficiency. Numerical results demonstrating the theoretical error estimates are also presented in five examples.
Keywords
- Augmented Lagrangian techniques, High order finite element discretizations, Newton iterative methods, P-Laplace-type problems, Power-law diffusion problems
ASJC Scopus subject areas
- Mathematics(all)
- Computational Mathematics
- Mathematics(all)
- Applied Mathematics
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In: SIAM Journal on Scientific Computing, Vol. 39, No. 3, 2017, p. A681-A710.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Numerical methods for power-law diffusion problems
AU - Toulopoulos, Ioannis
AU - Wick, Thomas
N1 - Publisher Copyright: © 2017 Society for Industrial and Applied Mathematics. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.
PY - 2017
Y1 - 2017
N2 - In this paper, we consider numerical methods for nonlinear diffusion problems where the diffusion term follows a power law, e.g., p-Laplace-type problems. In the first part, we present continuous higher order finite element discretizations for the model problem and we derive error estimates. In the second part, we discuss Newton iterative methods based on residual-based linesearch and error-oriented globalization, which are employed for the numerical solution of the produced nonlinear algebraic system. Third, we formulate the original problem as a saddle point problem in the frame of augmented Lagrangian techniques and present two iterative methods for its solution. We conduct a systematic investigation of all solution algorithms. These algorithms are compared with respect to computational cost and their efficiency. Numerical results demonstrating the theoretical error estimates are also presented in five examples.
AB - In this paper, we consider numerical methods for nonlinear diffusion problems where the diffusion term follows a power law, e.g., p-Laplace-type problems. In the first part, we present continuous higher order finite element discretizations for the model problem and we derive error estimates. In the second part, we discuss Newton iterative methods based on residual-based linesearch and error-oriented globalization, which are employed for the numerical solution of the produced nonlinear algebraic system. Third, we formulate the original problem as a saddle point problem in the frame of augmented Lagrangian techniques and present two iterative methods for its solution. We conduct a systematic investigation of all solution algorithms. These algorithms are compared with respect to computational cost and their efficiency. Numerical results demonstrating the theoretical error estimates are also presented in five examples.
KW - Augmented Lagrangian techniques
KW - High order finite element discretizations
KW - Newton iterative methods
KW - P-Laplace-type problems
KW - Power-law diffusion problems
UR - http://www.scopus.com/inward/record.url?scp=85021822089&partnerID=8YFLogxK
U2 - 10.1137/16m1067792
DO - 10.1137/16m1067792
M3 - Article
AN - SCOPUS:85021822089
VL - 39
SP - A681-A710
JO - SIAM Journal on Scientific Computing
JF - SIAM Journal on Scientific Computing
SN - 1064-8275
IS - 3
ER -