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Variational Approximation for a Non-Isothermal Coupled Phase-Field System: Structure-Preservation & Nonlinear Stability / Brunk, Aaron (Rights reserved)

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Periodical

Title:
Computational methods in applied mathematics
Publication:
Berlin: De Gruyter
Note:
Gesehen am 29.01.13
355!URL mit z LF gelöscht(19-01-13)
Scope:
Online-Ressource
ISSN:
1609-9389
ZDB-ID:
2075629-X ZDB
VÖBB-Katalog:
34851710
Keywords:
Zeitschrift
Classification:
Mathematik
Collection:
Mathematik
Copyright:
Rights reserved
Accessibility:
Eingeschränkter Zugang mit Nutzungsbeschränkungen
Title:
Computational methods in applied mathematics
Publication:
Berlin: De Gruyter
Note:
Gesehen am 29.01.13
355!URL mit z LF gelöscht(19-01-13)
Scope:
Online-Ressource
ISSN:
1609-9389
ZDB-ID:
2075629-X ZDB
VÖBB-Katalog:
34851710
Keywords:
Zeitschrift
Classification:
Mathematik
Collection:
Mathematik
Copyright:
Rights reserved
Accessibility:
Eingeschränkter Zugang mit Nutzungsbeschränkungen

Article

Author:
Brunk, Aaron
Habrich, Oliver
Oyedeji, Timileyin David
Yang, Yangyiwei
Xu, Bai-Xiang
Title:
Variational Approximation for a Non-Isothermal Coupled Phase-Field System: Structure-Preservation & Nonlinear Stability
Publication:
Berlin: De Gruyter, 2025
Language:
English
Information:
Abstract: A Cahn–Hilliard–Allen–Cahn phase-field model coupled with a heat transfer equation, particularly with full non-diagonal mobility matrices, is studied. After reformulating the problem with respect to the inverse of temperature, we proposed and analysed a structure-preserving approximation for the semi-discretisation in space and then a fully discrete approximation using conforming finite elements and time-stepping methods. We prove structure-preserving property and discrete stability using relative entropy methods for the semi-discrete and fully discrete case. The theoretical results are illustrated by numerical experiments.
Scope:
Online-Ressource
Note:
Kein Open Access
Archivierung/Langzeitarchivierung gewährleistet
Keywords:
Non-Isothermal Phase-Field ; Cross-Diffusion ; Finite Elements ; Entropy Stable ; 65M60 ; 35K52 ; 35K55 ; 65M12 ; 82C26
Classification:
Mathematik
Sonstiges
URN:
urn:nbn:de:101:1-2503300631201.257254126864
Collection:
Mathematik
Sonstiges
Copyright:
Rights reserved
Accessibility:
Eingeschränkter Zugang mit Nutzungsbeschränkungen
Author:
Brunk, Aaron
Habrich, Oliver
Oyedeji, Timileyin David
Yang, Yangyiwei
Xu, Bai-Xiang
Title:
Variational Approximation for a Non-Isothermal Coupled Phase-Field System: Structure-Preservation & Nonlinear Stability
Publication:
Berlin: De Gruyter, 2025
Language:
English
Information:
Abstract: A Cahn–Hilliard–Allen–Cahn phase-field model coupled with a heat transfer equation, particularly with full non-diagonal mobility matrices, is studied. After reformulating the problem with respect to the inverse of temperature, we proposed and analysed a structure-preserving approximation for the semi-discretisation in space and then a fully discrete approximation using conforming finite elements and time-stepping methods. We prove structure-preserving property and discrete stability using relative entropy methods for the semi-discrete and fully discrete case. The theoretical results are illustrated by numerical experiments.
Scope:
Online-Ressource
Note:
Kein Open Access
Archivierung/Langzeitarchivierung gewährleistet
Keywords:
Non-Isothermal Phase-Field ; Cross-Diffusion ; Finite Elements ; Entropy Stable ; 65M60 ; 35K52 ; 35K55 ; 65M12 ; 82C26
Classification:
Mathematik
Sonstiges
URN:
urn:nbn:de:101:1-2503300631201.257254126864
Collection:
Mathematik
Sonstiges
Copyright:
Rights reserved
Accessibility:
Eingeschränkter Zugang mit Nutzungsbeschränkungen

Contents

Table of contents

  • Computational methods in applied mathematics (Rights reserved)
  • Nonlinear Elastic-Net Regularization and Its Iterative Soft Thresholding Algorithm / Tian, Yu (Rights reserved)
  • Error Estimates of Scalar Auxiliary Variable Schemes with Variable Time Steps for the Magneto-Hydrodynamic Equations / Mu, Yuanyuan (Rights reserved)
  • Error Analysis of BDF2 Scheme for the Boussinesq System Based on Exponential Scalar Auxiliary Variable / Li, Huanhuan (Rights reserved)
  • Anderson–Picard Based Nonlinear Preconditioning of the Newton Iteration for Non-Isothermal Flow Simulations / Hawkins, Elizabeth (Rights reserved)
  • A Parametric Finite Element Method for a Degenerate Multi-Phase Stefan Problem with Triple Junctions / Eto, Tokuhiro (Rights reserved)
  • A Posteriori Error Analysis of the Virtual Element Method for Second-Order Quasilinear Elliptic PDEs / Congreve, Scott (Rights reserved)
  • Finite Volume Methods for Two-Dimensional Nonlocal Partial Differential Equation with a Gradient Flow Structure / Cai, Wenli (Rights reserved)
  • Frontmatter (Rights reserved)
  • A Class of Meshless Structure-Preserving Algorithms for the Nonlinear Schrödinger Equation / Wang, Jialing (Rights reserved)
  • Convergence Rates for a Finite Volume Scheme of the Stochastic Heat Equation / Sapountzoglou, Niklas (Rights reserved)
  • A Conservative Eulerian Finite Element Method for Transport and Diffusion in Moving Domains / Olshanskii, Maxim (Rights reserved)
  • A Potential-Robust WG Finite Element Method for the Maxwell Equations on Tetrahedral Meshes / Nie, Yufeng (Rights reserved)
  • Semi- and Fully-Discrete Analysis of Lowest-Order Nonstandard Finite Element Methods for the Biharmonic Wave Problem / Nataraj, Neela (Rights reserved)
  • Simplified Iterated Lavrentiev Regularization in Hilbert Scales / Mahale, Pallavi (Rights reserved)
  • Two Regularization Methods for Identifying the Initial Value of Time-Fractional Telegraph Equation / Liang, Ying-Qing (Rights reserved)
  • Guaranteed Lower and Upper Bounds for Eigenvalues of Second Order Elliptic Operators in any Dimension / Hu, Jun (Rights reserved)
  • A Galerkin Approach to the Generalized Karush–Kuhn–Tucker Conditions for the Solution of an Elliptic Distributed Optimal Control Problem with Pointwise State and Control Constraints / Brenner, Susanne C. (Rights reserved)
  • A Hodge Decomposition Finite Element Method for an Elliptic Maxwell Boundary Value Problem on General Polyhedral Domains / Brenner, Susanne C. (Rights reserved)
  • Analysis and Systematic Discretization of a Fokker–Planck Equation with Lorentz Force / Bosboom, Vincent (CC BY)
  • An hp -Adaptive Strategy Based on Locally Predicted Error Reductions / Bammer, Patrick (CC BY)
  • A Nested Uzawa Solver for a Dual-Dual Mixed Finite Element Method for Frictional Contact Problems in Linear Elasticity / Andres, Michael (Rights reserved)
  • Frontmatter (Rights reserved)
  • High-Order Accurate Structure-Preserving Finite Volume Scheme for Ten-Moment Gaussian Closure Equations with Source Terms: Positivity and Well-Balancedness / Zhang, Zhihao (Rights reserved)
  • Guaranteed Upper Bounds for Iteration Errors and Modified Kačanov Schemes via Discrete Duality / Diening, Lars (Rights reserved)
  • Robust Multigrid Methods for Discontinuous Galerkin Discretizations of an Elliptic Optimal Control Problem / Liu, Sijing (Rights reserved)
  • 8th Chinese–German Workshop on Computational and Applied Mathematics / Braack, Malte (Rights reserved)
  • On Error Estimates of a Discontinuous Galerkin Method of the Boussinesq System of Equations / Bajpai, Saumya (Rights reserved)
  • A P 2 H-Div-Nonconforming-H-Curl Finite Element for the Stokes Equations on Triangular Meshes / Huang, Yunqing (Rights reserved)
  • Mapped Coercivity for the Stationary Navier–Stokes Equations and Their Finite Element Approximations / Becker, Roland (Rights reserved)
  • A Staggered Discontinuous Galerkin Method for the Simulation of Wave Propagation in Poroelastic Media / Zhao, Lina (Rights reserved)
  • A Note on the Quasi-Best Approximation Constant / Carstensen, Carsten (Rights reserved)
  • Anisotropic Adaptive Finite Elements for a p -Laplacian Problem / Passelli, Paride (CC BY)
  • Analysis of a Combined Spherical Harmonics and Discontinuous Galerkin Discretization for the Boltzmann Transport Equation / Assogba, Kenneth (Rights reserved)
  • ˜Theœ Partition of Unity Finite Element Method for the Schrödinger Equation / Boffi, Daniele (CC BY)
  • Frontmatter (Rights reserved)
  • Frontmatter (Rights reserved)
  • A Space-Time Finite Element Method for the Eddy Current Approximation of Rotating Electric Machines / Gangl, Peter (Rights reserved)
  • A Mixed Finite Element Method for Coupled Plates / Hu, Jun (Rights reserved)
  • Contact Problems in Porous Media / Banz, Lothar (Rights reserved)
  • Error Analysis of the Vector Penalty-Projection Methods for the Time-Dependent Stokes Equations with Open Boundary Conditions / Cheaytou, Rima (Rights reserved)
  • An Inverse Matrix Eigenvalue Problem for Constructing a Vibrating Rod / Mirzaei, Hanif (Rights reserved)
  • Frontmatter (Rights reserved)
  • On an Optimal AFEM for Elastoplasticity / Schönauer, Miriam (CC BY)
  • A Finite Element Analysis in Balanced Norms for a Coupled System of Singularly Perturbed Reaction-Diffusion Equations / Armentano, María Gabriela (Rights reserved)
  • A Novel Fully Decoupled Scheme for the MHD System with Variable Density / Wang, Zhaowei (Rights reserved)
  • Machine Learning Estimators: Implementation and Comparison in Python / Merle, Fabian (Rights reserved)
  • Numerical Analysis of a Second-Order Algorithm for the Time-Dependent Natural Convection Problem / Chen, Yiru (Rights reserved)
  • A Streamline Upwind Petrov-Galerkin Reduced Order Method for Advection-Dominated Partial Differential Equations Under Optimal Control / Zoccolan, Fabio (Rights reserved)
  • Variational Approximation for a Non-Isothermal Coupled Phase-Field System: Structure-Preservation & Nonlinear Stability / Brunk, Aaron (Rights reserved)
  • Discontinuous Galerkin Methods for the Vlasov–Stokes System / Hutridurga, Harsha (Rights reserved)
  • Computing Both Upper and Lower Eigenvalue Bounds by HDG Methods / Liang, Qigang (Rights reserved)
  • Convergence of an Operator Splitting Scheme for Fractional Conservation Laws with Lévy Noise / Behera, Soumya Ranjan (Rights reserved)
  • Finite Element Formulations for Maxwell’s Eigenvalue Problem Using Continuous Lagrangian Interpolations / Boffi, Daniele (Rights reserved)
  • Super-Localized Orthogonal Decomposition Method for Heterogeneous Linear Elasticity / Belponer, Camilla (Rights reserved)
  • A Numerical Study of a Stabilized Hyperbolic Equation Inspired by Models for Bio-Polymerization / Davis, Lisa (Rights reserved)
  • Quadratic Discontinuous Galerkin Finite Element Methods for the Unilateral Contact Problem / Porwal, Kamana (Rights reserved)
  • In Memoriam of Raytcho Lazarov / Iliev, Oleg (Rights reserved)
  • Asymptotic Preserving Semi-Implicit Scheme for the Shallow Water Equations with Non-Flat Bottom Topography and Manning Friction Term / Huang, Guanlan (Rights reserved)
  • Tensor-Product Vertex Patch Smoothers for Biharmonic Problems / Witte, Julius (Rights reserved)
  • Analysis and Numerical Simulation of Time-Fractional Derivative Contact Problem with Friction in Thermo-Viscoelasticity / Bouallala, Mustapha (Rights reserved)
  • HDG Method for Nonlinear Parabolic Integro-Differential Equations / Jain, Riya (Rights reserved)
  • Quasi-Optimality of an AFEM for General Second Order Elliptic PDE / Pal, Arnab (Rights reserved)
  • Frontmatter (Rights reserved)
  • Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 2) / Feischl, Michael (Rights reserved)
  • Wave Propagation in High-Contrast Media: Periodic and Beyond / Fressart, Élise (Rights reserved)
  • A Phase-Space Discontinuous Galerkin Scheme for the Radiative Transfer Equation in Slab Geometry / Bardin, Riccardo (CC BY)
  • Numerical Approximation of Gaussian Random Fields on Closed Surfaces / Bonito, Andrea (Rights reserved)
  • Adaptive Image Compression via Optimal Mesh Refinement / Feischl, Michael (CC BY)
  • Weak Convergence of the Rosenbrock Semi-implicit Method for Semilinear Parabolic SPDEs Driven by Additive Noise / Mukam, Jean Daniel (Rights reserved)
  • Convergence of Adaptive Crouzeix–Raviart and Morley FEM for Distributed Optimal Control Problems / Dond, Asha K. (Rights reserved)
  • Adaptive Multi-level Algorithm for a Class of Nonlinear Problems / Kim, Dongho (CC BY)
  • Efficient P1-FEM for Any Space Dimension in Matlab / Beuter, Stefanie (Rights reserved)
  • Space-Time FEM for the Vectorial Wave Equation under Consideration of Ohm’s Law / Hauser, Julia I. M. (Rights reserved)
  • Computational Methods in Applied Mathematics (CMAM 2022 Conference, Part 1) / Feischl, Michael (Rights reserved)
  • Frontmatter (Rights reserved)
  • Robust PRESB Preconditioning of a 3-Dimensional Space-Time Finite Element Method for Parabolic Problems / Foltyn, Ladislav (Rights reserved)
  • Simultaneous Reconstruction of Speed of Sound and Nonlinearity Parameter in a Paraxial Model of Vibro-Acoustography in Frequency Domain / Kaltenbacher, Barbara (CC BY)
  • Error Identities for Parabolic Equations with Monotone Spatial Operators / Repin, Sergey I. (Rights reserved)
  • Space-Time Least-Squares Finite Element Methods for Parabolic Distributed Optimal Control Problems / Führer, Thomas (Rights reserved)
  • A Data-Driven Method for Parametric PDE Eigenvalue Problems Using Gaussian Process with Different Covariance Functions / Alghamdi, Moataz (Rights reserved)
  • An Optimal Method for High-Order Mixed Derivatives of Bivariate Functions / Semenova, Evgeniya V. (Rights reserved)
  • Frontmatter (Rights reserved)
  • Frontmatter (Rights reserved)

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