Related papers: An algorithm for one-dimensional Generalized Porou…
This paper presents a new finite difference method, called {\varphi}-FD, inspired by the {\phi}-FEM approach for solving elliptic partial differential equations (PDEs) on general geometries. The proposed method uses Cartesian grids,…
We show that optimal $L^2$-convergence in the finite element method on quasi-uniform meshes can be achieved if, for some $s_0 > 1/2$, the boundary value problem has the mapping property $H^{-1+s} \rightarrow H^{1+s}$ for $s \in [0,s_0]$.…
This work develops an epsilon-uniform finite element method for singularly perturbed boundary value problems. A surprising and remarkable observation is illustrated: By moving one node arbitrarily in between its adjacent nodes, the new…
Trace finite element methods have become a popular option for solving surface partial differential equations, especially in problems where surface and bulk effects are coupled. In such methods a surface mesh is formed by approximately…
In this paper, we first prove a localized Hamilton-type gradient estimate for the positive solutions of Porous Media type equations: $$u_t=\Delta F(u),$$ with $F'(u) > 0$, on a complete Riemannian manifold with Ricci curvature bounded from…
We consider an 1D partial integro-differential equation (PIDE) comprising of an 1D parabolic partial differential equation (PDE) and a nonlocal integral term. The control input is applied on one of the boundaries of the PIDE. Partitioning…
We formulate a general shape and topology optimization problem in structural optimization by using a phase field approach. This problem is considered in view of well-posedness and we derive optimality conditions. We relate the diffuse…
We prove bounds on statistical distances between high-dimensional exchangeable mixture distributions (which we call \emph{permutation mixtures}) and their i.i.d. counterparts. Our results are based on a novel method for controlling $\chi^2$…
A system of singularly perturbed ordinary differential equations of first order with given initial conditions is considered. The leading term of each equation is multiplied by a small positive parameter. These parameters are assumed to be…
Near-horizon symmetries are studied for static black hole solutions to Einstein equations containing supertranslation field. We consider general diffeomorphisms which preserve the gauge and the near-horizon structure of the metric.…
A simple and efficient interface-fitted mesh generation algorithm is developed in this paper. This algorithm can produce a local anisotropic fitting mixed mesh which consists of both triangles and quadrilaterals near the interface. A new…
We present an algorithm for treating mesh refinement interfaces in numerical relativity. We detail the behavior of the solution near such interfaces located in the strong field regions of dynamical black hole spacetimes, with particular…
A fractured poroelastic body is considered where the opening of the fractures is governed by a nonpenetration law while slip is described by a Coulomb-type friction law. This physical model results in a nonlinear variational inequality…
A wide variety of interface capturing methods have been introduced for simulating two-phase flows throughout the years. However, there is a noticeable dearth of literature focusing on objective comparisons between these methods, especially…
Polygonal finite elements generally do not pass the patch test as a result of quadrature error in the evaluation of weak form integrals. In this work, we examine the consequences of lack of polynomial consistency and show that it can lead…
We propose a nonlinear Discrete Duality Finite Volume scheme to approximate the solutions of drift diffusion equations. The scheme is built to preserve at the discrete level even on severely distorted meshes the energy / energy dissipation…
In this paper, a multiscale approach with partially explicit time discretization is proposed. The idea is to use a partially explicit time scheme, considering a filtration problem in a fractured medium, where the implicit scheme is used for…
We compare two singularly perturbed elliptic systems modeling partially phase segregation. Although the formulations are fundamentally different, we prove that their limiting configurations have identical free boundaries. The result shows…
In this paper, we define new unfitted finite element methods for numerically approximating the solution of surface partial differential equations using bulk finite elements. The key idea is that the $n$-dimensional hypersurface, $\Gamma…
We consider fourth order singularly perturbed boundary value problems with two small parameters, and the approximation of their solution by the $hp$ version of the Finite Element Method on the {\emph{Spectral Boundary Layer}} mesh from…