A posteriori error control for the Allen–Cahn problem: circumventing Gronwall's inequality

By D. Kessler, Ricardo H. Nochetto, Alfred Schmidt. 2004

158 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Computational Theory and Mathematics, Materials Chemistry

View Paper: https://www.semanticscholar.org/paper/423969d454bd48b093d9be55dcf98607cd9ff6cf

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Aerospace Engineering

1. Xiaofeng Yang
2. Jie Shen
3. Jie Xu
4. Junseok Kim
5. Hao Wu

In Computational Theory and Mathematics

1. Xiaofeng Yang
2. Jie Shen
3. Jie Xu
4. Jiang Yang
5. Tao Tang
6. Jia Zhao
7. Qi Wang
8. Xinlong Feng

In Materials Chemistry

1. Jie Shen
2. Xiaofeng Yang
3. Jie Xu
4. Jia Zhao
5. Jiang Yang
6. Qi Wang
7. Tao Tang
8. Qiang Du

Citations in the corpus

• Convergence and Error Analysis for the Scalar Auxiliary Variable (SAV) Schemes to Gradient Flows (2018, background): “Although some convergence and error analysis are available for fully implicit (such as backward Euler) [7, 10, 23, 11, 5] or nonlinearly implicit (such as convex splitting) [9, 2] schemes without restrictive assumptions on the free energy, most of the convergence and error analysis for linearly impl”
• Energy stable schemes for Cahn-Hilliard phase-field model of two-phase incompressible flows (2010, methodology): “Therefore, it has been a common practice to consider the Cahn-Hilliard equation with a truncated double-well potential F (φ) (cf. [13] [6]).”
• Analysis of interior penalty discontinuous Galerkin methods for the Allen-Cahn equation and the mean curvature flow (2013, unknown): “In addition, polynomial order in 1 a posteriori error estimates were obtained in [16, 13, 3].”
• Numerical approximations of Allen-Cahn and Cahn-Hilliard equations (2010, background): “[15, 8]) to consider the Allen-Cahn and Cahn-Hilliard equations with a truncated double-well potential F (u).”
• Error analysis of stabilized semi-implicit method of Allen-Cahnequation (2009, unknown): “The schemes (2) and (3) first appeared in [8, 9, 18, 19].”
• The phase field method for geometric moving interfaces and their numerical approximations (2019, unknown): “A topological argument was used in [285], in which the PDE spectral estimate is embedded, to obtain a fine a posteriori error bound; while a sharp continuous dependence estimate for the PDE solution was used, in which the PDE spectral estimate was crucially utilized, to derive fine a posteriori erro”