Harald Garcke
- Thermodynamically Consistent, Frame Indifferent Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities
2011/01/01 by Helmut Abels, Abels, H., Harald Garcke +3 · 15 citations
Computer Science · Engineering · #35Q30 #35Q35 #35R35 #76D05 #76D45 #76T99 #80A22 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Thin Films #Lattice Boltzmann Simulation Studies
- Finite Element Approximation of the Cahn--Hilliard Equation with Degenerate Mobility
1999/01/01 by John W. Barrett, James F. Blowey, Harald Garcke · 7 citations
Materials Science · Computer Science · Mathematics · #Solidification and crystal growth phenomena #Advanced Mathematical Modeling in Engineering #Differential Equations and Numerical Methods
- Analysis of a Cahn-Hilliard-Brinkman model for tumour growth with\n chemotaxis
2018/07/02 by Matthias Ebenbeck, Ebenbeck, Matthias, Harald Garcke +1 · 6 citations
Computer Science · Materials Science · #35D30 #35K35 #35Q92 #76D07 #92C50 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Solidification and crystal growth phenomena
- Global regularity and asymptotic stabilization for the incompressible Navier-Stokes-Cahn-Hilliard model with unmatched densities
2022/09/22 by Helmut Abels, Abels, Helmut, Harald Garcke +2 · 7 citations
Mathematics · Materials Science · #Navier-Stokes equation solutions #Solidification and crystal growth phenomena #Nonlinear Partial Differential Equations
- Well-posedness of a Cahn--Hilliard system modelling tumour growth with\n chemotaxis and active transport
2015/11/19 by Harald Garcke, Garcke, Harald, Kei Fong Lam +1 · 3 citations
Computer Science · Materials Science · Mathematics · #35K50 #35K57 #35Q92 #92B05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Biological sciences #FOS: Mathematics #Mathematical Biology Tumor Growth #Solidification and crystal growth phenomena #Tissues and Organs (q-bio.TO)
- Optimal control of treatment time in a diffuse interface model of tumor\n growth
2016/08/01 by Harald Garcke, Kei-Fong Lam, Garcke, Harald +3 · 2 citations
Mathematics · Computer Science · Materials Science · #Mathematical Biology Tumor Growth #Advanced Mathematical Modeling in Engineering #Solidification and crystal growth phenomena
- Global weak solutions and asymptotic limits of a Cahn--Hilliard--Darcy\n system modelling tumour growth
2016/08/31 by Harald Garcke, Kei Fong Lam, Garcke, Harald +1 · 1 citation
Mathematics · Materials Science · #Nonlinear Partial Differential Equations #Solidification and crystal growth phenomena
- Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase\n Flow with Surfactants
2017/10/09 by Helmut Abels, Harald Garcke, Abels, Helmut +3 · 1 citation
Engineering · Mathematics · #Fluid Dynamics and Thin Films #Lattice Boltzmann Simulation Studies #Navier-Stokes equation solutions
- On a Cahn-Hilliard-Brinkman model for tumour growth and its singular limits
2018/11/16 by Matthias Ebenbeck, Harald Garcke, Ebenbeck, Matthias +1 · 1 citation
Computer Science · Mathematics · #35D30 #35K35 #35Q92 #76D07 #92C50 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Biology Tumor Growth #Nonlinear Partial Differential Equations
- Numerical analysis for the interaction of mean curvature flow and diffusion on closed surfaces
2022/01/01 by Charles M. Elliott, Elliott, Charles M., Harald Garcke +3 · 2 citations
Computer Science · Engineering · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Contact Mechanics and Variational Inequalities #FOS: Mathematics #Numerical Analysis (math.NA)
- Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Local Well-Posedness
2024/07/20 by Helmut Abels, Harald Garcke, Abels, Helmut +3 · 2 citations
Computer Science · Engineering · #35D35 #35Q30 #35Q35 #76D05 #76T06 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Lattice Boltzmann Simulation Studies
- Diffuse Interface Model for Two-Phase Flows on Evolving Surfaces with Different Densities: Global Well-Posedness
2024/08/14 by Helmut Abels, Harald Garcke, Abels, Helmut +3 · 2 citations
Computer Science · Engineering · #35D35 #35Q30 #35Q35 #76D05 #76T06 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Heat Transfer #Fluid Dynamics and Thin Films
- Structure-preserving parametric finite element method for curve diffusion based on Lagrange multiplier approaches
2024/08/24 by Harald Garcke, Garcke, Harald, Wei Jiang +5 · 1 citation
Engineering · #35K55 #53C44 #65M12 #65M60 #Advanced Numerical Analysis Techniques #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods in engineering
- Convergence analysis for the Barrett--Garcke--Nurnberg method of transport type for evolving curves
2025/09/09 by Genming Bai, Harald Garcke, Bai, Genming +3 · 2 citations
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #FOS: Mathematics #Numerical Analysis (math.NA) #Numerical methods for differential equations
- Diffuse Interface Models for Two-Phase Flows with Phase Transition: Modeling and Existence of Weak Solutions
2025/05/08 by Helmut Abels, Harald Garcke, Abels, Helmut +2 · 2 citations
Engineering · Materials Science · Mathematics · #35D35 #35Q30 #35Q35 #76D05 #76T06 #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Thin Films #Navier-Stokes equation solutions #Solidification and crystal growth phenomena
- The anisotropic Cahn--Hilliard equation with degenerate mobility: Existence of weak solutions
2025/02/19 by Harald Garcke, Garcke, Harald, Patrik Knopf +3 · 1 citation
Computer Science · Materials Science · Mathematics · #35D30 #35K55 #35K61 #74E10 #82C26 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Solidification and crystal growth phenomena