Malte Braack
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View article: Well-posedness of the Stokes problem under modified pressure Dirichlet boundary conditions
Well-posedness of the Stokes problem under modified pressure Dirichlet boundary conditions Open
This paper shows that the Stokes problem is well-posed when velocity and pressure simultaneously vanish on the domain boundary. This result is achieved by extending Nečas’ inequality to square-integrable functions that vanish in a small ba…
View article: NN-TOC v1: global prediction of total organic carbon in marine sediments using deep neural networks
NN-TOC v1: global prediction of total organic carbon in marine sediments using deep neural networks Open
Spatial predictions of total organic carbon (TOC) concentrations and stocks are crucial for understanding marine sediments’ role as a significant carbon sink in the global carbon cycle. In this study, we present a geospatial prediction of …
View article: The concept of mapped coercivity for nonlinear operators in Banach spaces
The concept of mapped coercivity for nonlinear operators in Banach spaces Open
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View article: Inf-sup condition for Stokes with outflow condition
Inf-sup condition for Stokes with outflow condition Open
The inf-sup condition is one of the essential tools in the analysis of the Stokes equations and especially in numerical analysis. In its usual form, the condition states that for every pressure $p\in L^2(Ω)\setminus \mathbb{R}$, (i.e. with…
View article: Optimized Predator‐Prey and MPA Based Fishing Strategies for the Baltic Sea
Optimized Predator‐Prey and MPA Based Fishing Strategies for the Baltic Sea Open
Marine protected areas (MPAs) have become the de‐facto mechanism for marine species conservation and management and the ecological benefits of no take zones (NTZs) are supported by an expanding scientific interest in their effectiveness. H…
View article: Mapped coercivity for the stationary Navier-Stokes equations and their finite element approximations
Mapped coercivity for the stationary Navier-Stokes equations and their finite element approximations Open
This paper addresses the challenge of proving the existence of solutions for nonlinear equations in Banach spaces, focusing on the Navier-Stokes equations and discretizations of thom. Traditional methods, such as monotonicity-based approac…
View article: NN-TOC v1: global prediction of total organic carbon in marine sediments using deep neural networks
NN-TOC v1: global prediction of total organic carbon in marine sediments using deep neural networks Open
Spatial predictions of total organic carbon (TOC) concentrations and stocks are crucial for understanding marine sediments’ role as a significant carbon sink in the global carbon cycle. In this study, we present a geospatial prediction of …
View article: Predicting Global Seafloor Organic Carbon Burial Rates: A Deep Learning Approach with Uncertainty Quantification
Predicting Global Seafloor Organic Carbon Burial Rates: A Deep Learning Approach with Uncertainty Quantification Open
Sediment accumulation rate is recognized as the primary parameter influencing the burial rate of organic carbon and other compounds in marine sediments. The prediction of a global map for burial rates is challenging due to the limited avai…
View article: An adaptive moving finite element method for steady low Mach number compressible combustion problems
An adaptive moving finite element method for steady low Mach number compressible combustion problems Open
This work surveys an r‐adaptive moving mesh finite element method for the numerical solution of premixed laminar flame problems. Since the model of chemically reacting flow involves many different modes with diverse length scales, the comp…
View article: Global Prediction Of Total Organic Carbon In Marine Sediments Using (Software) Deep Neural Networks (nn-toc)
Global Prediction Of Total Organic Carbon In Marine Sediments Using (Software) Deep Neural Networks (nn-toc) Open
We create a deep neural network based approach for the geospatial predicition of total organic carbon percentages in marine sediments. The code in the repository includes jupyter notebooks and python files to pre-process the data, train th…
View article: The concept of mapped coercivity for nonlinear operators in Banach spaces
The concept of mapped coercivity for nonlinear operators in Banach spaces Open
We provide a concise proof of existence for nonlinear operator equations in separable Banach spaces. Notably, the operator is not assumed to be monotone. Instead, our main hypotheses consist of a continuity assumption and a generalized coe…
View article: Semi-supervised feature-based learning for prediction of Mass Accumulation Rate of sediments
Semi-supervised feature-based learning for prediction of Mass Accumulation Rate of sediments Open
Mass accumulation rates of sediments[g/cm2/yr] or sedimentation rates[cm/yr] on the seafloor are important to understand various benthic properties, like the rate of carbon sequestration in the seafloor and seafloor geomechanical stability…
View article: Sino–German Computational and Applied Mathematics
Sino–German Computational and Applied Mathematics Open
This short article serves as an epilog of the thirteen preceding papers in this special issue of CMAM. All contributions are authored by participants of the 7th Sino–German Workshop on Computational and Applied Mathematics at the Kiel Univ…
View article: Local pressure‐correction for the Navier‐Stokes equations
Local pressure‐correction for the Navier‐Stokes equations Open
This article presents a novel local pressure correction method for incompressible fluid flows and documents a numerical study of this method. Pressure correction methods decouple the velocity and pressure components of the time‐dependent N…
View article: Equal-order finite element approximation for mantle-melt transport
Equal-order finite element approximation for mantle-melt transport Open
Mantle convection and melt migration are important processes for understanding Earth’s dynamics and how they relate to observations at the surface. Recently it has been established that melt migration can be modelled by coupling variable-v…
View article: Equal-Order Stabilized Finite Element Approximation of the <i>p</i>-Stokes Equations on Anisotropic Cartesian Meshes
Equal-Order Stabilized Finite Element Approximation of the <i>p</i>-Stokes Equations on Anisotropic Cartesian Meshes Open
The p -Stokes equations with power-law exponent p ∈ ( 1 , 2 ) {p\in(1,2)} describes non-Newtonian, shear-thinning, incompressible flow. In many industrial applications and natural settings, shear-thinning flow takes place in very thi…
View article: Benchmark problems for numerical treatment of backflow at open boundaries
Benchmark problems for numerical treatment of backflow at open boundaries Open
In computational fluid dynamics, incoming velocity at open boundaries, or backflow , often yields unphysical instabilities already for moderate Reynolds numbers. Several treatments to overcome these backflow instabilities have been propose…