Related papers: Discontinuities without discontinuity: The Weakly-…
The locally modified finite element method, which is introduced in [Frei, Richter: SINUM 52(2014), p. 2315-2334], is a simple fitted finite element method that is able to resolve weak discontinuities in interface problems. The method is…
In this paper we study the use of Virtual Element method for geomechanics. Our emphasis is on applications to reservoir simulations. The physical processes that form the reservoirs, such as sedimentation, erosion and faulting, lead to…
We present a discontinuous finite element method for the shallow water equations which exploits high-resolution realistic bathymetry data without any regularity assumption, also in the case of high-order discretizations. We prove a number…
In this article, using the weighted discrete least-squares, we propose a patch reconstruction finite element space with only one degree of freedom per element. As the approximation space, it is applied to the discontinuous Galerkin methods…
We test methods for the determination of unstable modes in stellar discs: a point collocation scheme in the action sub-space, a scheme based on expansion of the density and potential on the biorthonormal basis, and a finite element method.…
In computational engineering, ensuring the integrity and safety of structures in fields such as aerospace and civil engineering relies on accurate stress prediction. However, analytical methods are limited to simple test cases, and…
The incidence of vertebral fragility fracture is increased by the presence of preexisting pathologies such as metastatic disease. Computational tools could support the fracture prediction and consequently the decision of the best medical…
To obtain fast solutions for governing physical equations in solid mechanics, we introduce a method that integrates the core ideas of the finite element method with physics-informed neural networks and concept of neural operators. This…
This paper introduces the Non-linear Partition of Unity Method, a novel technique integrating Radial Basis Function interpolation and Weighted Essentially Non-Oscillatory algorithms. It addresses challenges in high-accuracy approximations,…
Reduction of computational cost of solutions is a key issue to crack identification or crack propagation problems. One of the solution is to avoid re-meshing the domain when the crack position changes or when the crack extends. To avoid…
We solve elliptic systems of equations posed on highly heterogeneous materials. Examples of this class of problems are composite structures and geological processes. We focus on a model problem which is a second-order elliptic equation with…
Rotating the clamped ends of a buckled elastica induces a snap-through instability. Predicting the limit point and determining the equilibria at the start and end of the snap are routine computations in the quasi-static setting. The…
In floppy mechanical lattices, robust edge states and bulk Weyl modes are manifestations of underlying topological invariants. To explore the universality of these phenomena independent of microscopic detail, we formulate topological…
We propose an effective and flexible way to implement 2D and 3D elastoplastic problems in MATLAB using fully vectorized codes. Our technique is applied to a broad class of the problems including perfect plasticity or plasticity with…
In this article we present the numerical simulation of a dislocation incorporated into a Cosserat plate. The simulation is based on the mathematical model for bending of Cosserat elastic plates recently developed by the authors. The…
In engineering crystal plasticity inelastic mechanisms correspond to tensorial zero-energy valleys in the space of macroscopic strains. The flat nature of such valleys is in contradiction with the fact that plastic slips, mimicking…
Faults are complex systems embedded in an evolving medium fractured by seismic ruptures. This off-fault damage zone is shown to be thermo-hydro-mechano-chemically coupled to the main fault plane by a growing number of studies. Yet,…
In this paper, we study an affine connection approach to realizing nonholonomic mechanical systems mediated by viscous friction forces with large coefficients, viewed as a singular perturbation of the nonholonomic system. We show that the…
Strain gradient plasticity theories are being widely used for fracture assessment, as they provide a richer description of crack tip fields by incorporating the influence of geometrically necessary dislocations. Characterizing the behavior…
In this paper we present an immersed weak Galerkin method for solving second-order elliptic interface problems on polygonal meshes, where the meshes do not need to be aligned with the interface. The discrete space consists of constants on…