Related papers: Residual-based error estimation and adaptivity for…
Subdivision surfaces provide an elegant isogeometric analysis framework for geometric design and analysis of partial differential equations defined on surfaces. They are already a standard in high-end computer animation and graphics and are…
This article describes a full Bayesian treatment for simultaneous fixed-effect selection and parameter estimation in high-dimensional generalized linear mixed models. The approach consists of using a Bayesian adaptive Lasso penalty for…
Modern, powerful techniques for the residual analysis of spatial-temporal point process models are reviewed and compared. These methods are applied to California earthquake forecast models used in the Collaboratory for the Study of…
In this paper, the stabilized finite element method based on local projection is applied to discretize the Stokes eigenvalue problems and the corresponding convergence analysis is given. Furthermore, we also use a method to improve the…
Pixel- and voxel-based representations of microstructures obtained from tomographic imaging methods is an established standard in computational materials science. The corresponding highly resolved, uniform discretitization in numerical…
Anisotropic mesh adaptation has been successfully applied to the numerical solution of partial differential equations but little considered for variational problems. In this paper, we investigate the use of a global hierarchical basis error…
Lattice Boltzmann Methods (LBM) stand out for their simplicity and computational efficiency while offering the possibility of simulating complex phenomena. While they are optimal for Cartesian meshes, adapted meshes have traditionally been…
The Immersed Boundary method is a simple, efficient, and robust numerical scheme for solving PDE in general domains, yet for fluid problems it only achieves first-order spatial accuracy near embedded boundaries for the velocity field and…
An extension of the multi-level hp Finite Cell Method is proposed for the simulation of thermoviscoplastic problems with temperature-dependent material behavior. The approach combines hierarchical adaptive refinement with a non-negative…
A robust $hp$-adaptive finite element framework is presented for the investigation of static cracks in materials characterized by complex, pointwise density variations. Within such heterogeneous media, the equilibrium equation governed by…
This paper presents and analyzes an immersed finite element (IFE) method for solving Stokes interface problems with a piecewise constant viscosity coefficient that has a jump across the interface. In the method, the triangulation does not…
This work focuses on steady and unsteady Navier-Stokes equations in a reduced order modeling framework. The methodology proposed is based on a Proper Orthogonal Decomposition within a levelset geometry description and the problems of…
We study adaptive mesh selection for the solution of systems of initial value problems. The goal is a rigorous theoretical analysis of potential advantages of adaption. For an optimal method in the sense of the speed of convergence, we…
We consider locally stabilized, conforming finite element schemes on completely unstructured simplicial space-time meshes for the numerical solution of parabolic initial-boundary value problems with variable, possibly discontinuous in space…
This contribution investigates the connection between isogeometric analysis and integral equation methods for full-wave electromagnetic problems up to the low-frequency limit. The proposed spline-based integral equation method allows for an…
In this paper, we will outline a novel data-driven method for estimating functions in a multivariate nonparametric regression model based on an adaptive knot selection for B-splines. The underlying idea of our approach for selecting knots…
Binary-fluid flows can be modeled using the Navier-Stokes-Cahn-Hilliard equations, which represent the boundary between the fluid constituents by a diffuse interface. The diffuse-interface model allows for complex geometries and topological…
We develop and analyze a method for stochastic simulation optimization based on Gaussian process models within a trust-region framework. We focus on settings where the variance of the objective function is large, making accurate estimation…
Event cameras hold significant promise for high-temporal-resolution (HTR) motion estimation. However, estimating event-based HTR optical flow faces two key challenges: the absence of HTR ground-truth data and the intrinsic sparsity of event…
In this article we develop an $hp$-adaptive refinement procedure for Trefftz discontinuous Galerkin methods applied to the homogeneous Helmholtz problem. Our approach combines not only mesh subdivision (h-refinement) and local basis…