Related papers: A spatio-temporal adaptive phase-field fracture me…
We introduce a class of models based on near crack tip degradation of materials that can account for fracture growth under cyclic loads below the Griffith threshold. We incorporate the gradual degradation due to a cyclic load through a flow…
We develop all of the components needed to construct an adaptive finite element code that can be used to approximate fractional partial differential equations, on non-trivial domains in $d\geq 1$ dimensions. Our main approach consists of…
This is a study of certain finite element methods designed for convection-dominated, time-dependent partial differential equations. Specifically, we analyze high order space-time tensor product finite element discretizations, used in a…
This work uses a linear relaxation method to develop efficient numerical schemes for the time-fractional Allen-Cahn and Cahn-Hilliard equations. The L1+-CN formula is used to discretize the fractional derivative, and an auxiliary variable…
This work is concerned with the development of a space-time adaptive numerical method, based on a rigorous a posteriori error bound, for a semilinear convection-diffusion problem which may exhibit blow-up in finite time. More specifically,…
The governing equations of the variational approach to brittle and ductile fracture emerge from the minimization of a non-convex energy functional subject to irreversibility constraints. This results in a multifield problem governed by a…
We present the first method to directly use a learned continuous Lagrangian to forecast the dynamics of systems governed by partial differential equations, exploiting the inherent conservative structure to achieve stable long-range…
This work proposes a novel variational approximation of partial differential equations on moving geometries determined by explicit boundary representations. The benefits of the proposed formulation are the ability to handle large…
In variational phase-field modeling of brittle fracture, the functional to be minimized is not convex, so that the necessary stationarity conditions of the functional may admit multiple solutions. The solution obtained in an actual…
Despite its critical role in the study of earthquake processes, numerical simulation of the entire stages of fault rupture remains a formidable task. The main challenges in simulating a fault rupture process include complex evolution of…
In this work, we extend the recently proposed adaptive phase field method to model fracture in orthotropic functionally graded materials (FGMs). A recovery type error indicator combined with quadtree decomposition is employed for adaptive…
In this work, we bridge standard adaptive mesh refinement and coarsening on scalable octree background meshes and robust unfitted finite element formulations for the automatic and efficient solution of large-scale nonlinear solid mechanics…
In this paper we present an error analysis of an Eulerian finite element method for solving parabolic partial differential equations posed on evolving hypersurfaces in $\mathbb{R}^d$, $d=2,3$. The method employs discontinuous piecewise…
High-order implicit shock tracking (fitting) is a class of high-order, optimization-based numerical methods to approximate solutions of conservation laws with non-smooth features by aligning elements of the computational mesh with…
Efficient and energy stable high order time marching schemes are very important but not easy to construct for the study of nonlinear phase dynamics. In this paper, we propose and study two linearly stabilized second order semi-implicit…
We propose a variational phase-field model of fracture capable of accounting for arbitrary closed convex strength domains. Unlike traditional models based on Ambrosio and Tortorelli regularization, the phase-field variable does not affect…
We consider within a finite element approach the usage of different adaptively refined meshes for different variables in systems of nonlinear, time-depended PDEs. To resolve different solution behaviours of these variables, the meshes can…
In this work, we extend a phase-field approach for pressurized fractures to non-isothermal settings. Specifically, the pressure and the temperature are given quantities and the emphasis is on the correct modeling of the interface laws…
In this work, we present an adaptive unfitted finite element scheme that combines the aggregated finite element method with parallel adaptive mesh refinement. We introduce a novel scalable distributed-memory implementation of the resulting…
Modeling crack initiation and propagation in brittle materials is of great importance to be able to predict sudden loss of load-carrying capacity and prevent catastrophic failure under severe dynamic loading conditions. Second-order…