Related papers: Residual-based error estimation and adaptivity for…
Large deformation analysis in geomechanics plays an important role in understanding the nature of post-failure flows and hazards associated with landslides under different natural calamities. In this study, a SPH framework is proposed for…
The novel Locally Refined B-spline (LR B-spline) surface format is suited for representing terrain and seabed data in a compact way. It provides an alternative to the well know raster and triangulated surface representations. An LR B-spline…
A novel and efficient approach which is based on the framework of isogeometric analysis for elliptic homogenization problems is proposed. These problems possess highly oscillating coefficients leading to extremely high computational…
We propose a novel finite element method scheme for singularly perturbed advection-diffusion-reaction problems, which combines certain quantum-assisted stabilization scheme with a classical h-adaptive approach to provide automatic error…
The paper introduces an adaptive version of the stabilized Trace Finite Element Method (TraceFEM) designed to solve low-regularity elliptic problems on level-set surfaces using a shape-regular bulk mesh in the embedding space. Two…
We present a novel method named truncated hierarchical unstructured splines (THU-splines) that supports both local $h$-refinement and unstructured quadrilateral meshes. In a THU-spline construction, an unstructured quadrilateral mesh is…
An isogeometric boundary element method for problems in elasticity is presented, which is based on an independent approximation for the geometry, traction and displacement field. This enables a flexible choice of refinement strategies,…
A Skeleton-stabilized IsoGeometric Analysis (SIGA) technique is proposed for incompressible viscous flow problems with moderate Reynolds number. The proposed method allows utilizing identical finite dimensional spaces (with arbitrary…
Finite element methods based on cut-cells are becoming increasingly popular because of their advantages over formulations based on body-fitted meshes for problems with moving interfaces. In such methods, the cells (or elements) which are…
We present an online-adaptive hyperreduced reduced basis element method for model order reduction of parameterized, component-based nonlinear systems. The method, in the offline phase, prepares a library of hyperreduced archetype components…
This paper introduces a novel framework for model adaptivity in the context of heterogeneous multiscale problems. The framework is based on the idea to interpret model adaptivity as a minimization problem of local error indicators, that are…
Adaptive atomistic/continuum (a/c) coupling method is an important method for the simulation of material and atomistic systems with defects to achieve the balance of accuracy and efficiency. Residual based a posteriori error estimator is…
We use asymptotically optimal \emph{adaptive} numerical methods (here specifically a wavelet scheme) for snapshot computations within the offline phase of the Reduced Basis Method (RBM). The resulting discretizations for each snapshot…
This paper presents eigensolution and non-modal analyses for immersed boundary methods (IBMs) based on volume penalization for the linear advection equation. This approach is used to analyze the behavior of flux reconstruction (FR)…
This article presents an error analysis of the recently introduced Frenet immersed finite element (IFE) method. The Frenet IFE space employed in this method is constructed to be locally conforming to the function space of the associated…
An adaptive direct collocation method is developed for solving optimal control problems constrained by parabolic partial differential equations. The partial differential equation is first reformulated in a variational setting, where the…
This paper presents a mini immersed finite element (IFE) method for solving two- and three-dimensional two-phase Stokes problems on Cartesian meshes. The IFE space is constructed from the conventional mini element, with shape functions…
We propose and analyze optimal additive multilevel solvers for isogeometric discretizations of scalar elliptic problems for locally refined T-meshes. Applying the refinement strategy in Morgenstern and Peterseim (2015, Comput. Aided Geom.…
We introduce a new $hp$-adaptive strategy for self-adjoint elliptic boundary value problems that does not rely on using classical a posteriori error estimators. Instead, our approach is based on a generally applicable prediction strategy…
Isogeometric analysis is a recently developed framework based on finite element analysis, where the simple building blocks in geometry and solution space are replaced by more complex and geometrically-oriented compounds. Box splines are an…