71 citations · 75 across the 5 of their papers we have counts for
12 papers
Natural Factor Based Solvers
O. Andrés Cuervo, Juan Galvis, Marcus Sarkis
We consider parametric families of partial differential equations--PDEs where the parameter modifies only the (1,1) block of a saddle point matrix product of a discretization b…
From Additive Average Schwarz Methods to Non-overlapping Spectral Additive Schwarz Methods
Yi Yu, Maksymilian Dryja, Marcus Sarkis
In this paper, we design and analyze two new methods based on additive average Schwarz -- AAS method introduced in \cite{MR1943457}. The new methods design for elliptic problems wi…
An unconditionally stable semi-implicit CutFEM for an interaction problem between an elastic membrane and an incompressible fluid
Kyle Dunn, Roger Lui, Marcus Sarkis
In this paper we introduce a finite element method for the Stokes equations with a massless immersed membrane. This membrane applies normal and tangential forces affecting the velo…
Spectral ACMS: A robust localized Approximated Component Mode Synthesis Method
Alexandre L. Madureira, Marcus Sarkis
We consider finite element methods of multiscale type to approximate solutions for two-dimensional symmetric elliptic partial differential equations with heterogeneous c…
Hybrid Localized Spectral Decomposition for multiscale problems
Alexandre L. Madureira, Marcus Sarkis
We consider a finite element method for elliptic equation with heterogeneous and possibly high-contrast coefficients based on primal hybrid formulation. A space decomposition as in…
Analysis of the finite element method for the Laplace--Beltrami equation on surfaces with regions of high curvature using graded meshes
Johnny Guzman, Alexandre Madureira, Marcus Sarkis +1
We derive error estimates for the piecewise linear finite element approximation of the Laplace--Beltrami operator on a bounded, orientable, , surface without boundary on gener…
On high-order conservative finite element methods
Eduardo Abreu, Ciro Diaz, Juan Galvis +1
A new high-order conservative finite element method for Darcy flow is presented. The key ingredient in the formulation is a volumetric, residual-based, based on Lagrange multiplier…
Robust flux error estimation of an unfitted Nitsche method for high-contrast interface problems
Erik Burman, Johnny Guzman, Manuel A. Sanchez +1
We prove an optimal error estimate for the flux variable for a stabilized unfitted Nitsche finite element method applied to an elliptic interface problem with discontinuous constan…
A finite element method for high-contrast interface problems with error estimates independent of contrast
Johnny Guzman, Manuel A. Sanchez, Marcus Sarkis
We define a new finite element method for a steady state elliptic problem with discontinuous diffusion coefficients where the meshes are not aligned with the interface. We prove op…
Higher-order finite element methods for elliptic problems with interfaces
Johnny Guzman, Manuel A. Sanchez, Marcus Sarkis
We present higher-order piecewise continuous finite element methods for solving a class of interface problems in two dimensions. The method is based on correction terms added to th…
The analysis of FETI-DP preconditioner for full DG discretization of elliptic problems
Maksymilian Dryja, Juan Galvis, Marcus Sarkis
In this paper a discretization based on discontinuous Galerkin (DG) method for an elliptic two-dimensional problem with discontinuous coefficients is considered. The problem is pos…
Generalized Multiscale Finite Element Method. Symmetric Interior Penalty Coupling
Y. Efendiev, J. Galvis, R. Lazarov +2
Motivated by applications to numerical simulation of flows in highly heterogeneous porous media, we develop multiscale finite element methods for second order elliptic equations. W…