149 citations · 617 across the 22 of their papers we have counts for
22 papers
Elliptic reconstruction and a posteriori error estimates for fully discrete linear parabolic problems
Omar Lakkis, Charalambos Makridakis
We derive aposteriori error estimates for fully discrete approximations to solutions of linear parabolic equations on the space-time domain. The space discretization uses finite el…
A posteriori error estimates for the wave equation with mesh change in the leapfrog method
Marcus J. Grote, Omar Lakkis, Carina Santos
We derive a fully computable aposteriori error estimator for a Galerkin finite element solution of the wave equation with explicit leapfrog time-stepping. Our discrete formulation…
A least-squares Galerkin approach to gradient recovery for Hamilton-Jacobi-Bellman equation with Cordes coefficients
Omar Lakkis, Amireh Mousavi
We propose a conforming finite element method to approximate the strong solution of the second order Hamilton-Jacobi-Bellman equation with Dirichlet boundary and coefficients satis…
Parallel two-scale finite element implementation of a system with varying microstructures
Omar Richardson, Omar Lakkis, Adrian Muntean +1
We propose a two-scale finite element method designed for heterogeneous microstructures. Our approach exploits domain diffeomorphisms between the microscopic structures to gain com…
A least-squares Galerkin approach to gradient and Hessian recovery for nondivergence-form elliptic equations
Omar Lakkis, Amireh Mousavi
We propose a least-squares method involving the recovery of the gradient and possibly the Hessian for elliptic equation in nondivergence form. As our approach is based on the Lax--…
A finite element method for the Monge-Ampère equation with transport boundary conditions
Ellya Kawecki, Omar Lakkis, Tristan Pryer
We address the numerical solution via Galerkin type methods of the Monge-Ampère equation with transport boundary conditions arising in optimal mass transport, geometric optics and…
A posteriori error bounds for fully-discrete hp-discontinuous Galerkin timestepping methods for parabolic problems
Emmanuil H. Georgoulis, Omar Lakkis, Thomas P. Wihler
We consider fully discrete time-space approximations of abstract linear parabolic partial differential equations (PDEs) consisting of an -version discontinuous Galerkin (DG) ti…
A Saint-Venant shallow water model for overland flows with precipitation and recharge
Mehmet Ersoy, Omar Lakkis, Philip Townsend
We propose a one-dimensional Saint-Venant (open channel) model overland flows including a water input--output source term modelling recharge via rainfall and infiltration (or exfil…
A posteriori error estimates for leap-frog and cosine methods for second order evolution problems
Emmanuil H. Georgoulis, Omar Lakkis, Charalambos Makridakis +1
We consider second order explicit and implicit two-step time-discrete schemes for wave-type equations. We derive optimal order aposteriori estimates controlling the time discretiza…
An adaptive finite element method for the infinity Laplacian
Omar Lakkis, Tristan Pryer
We construct a finite element method (FEM) for the infinity Laplacian. Solutions of this problem may be singular, which has prompted us to conduct an a posteriori analysis of the m…
Adaptive finite elements for semilinear reaction-diffusion systems on growing domains
Chandrasekhar Venkataraman, Omar Lakkis, Anotida Madzvamuse
We propose an adaptive finite element method to approximate the solutions to reaction-diffusion systems on time-dependent domains and surfaces. We derive a computable error estimat…
Noise regularization and computations for the 1-dimensional stochastic Allen-Cahn problem
Markos A. Katsoulakis, Georgios T. Kossioris, Omar Lakkis
We address the numerical discretization of the Allen-Cahn prob- lem with additive white noise in one-dimensional space. The discretization is conducted in two stages: (1) regulariz…
Implicit-explicit timestepping with finite element approximation of reaction-diffusion systems on evolving domains
Omar Lakkis, Anotida Madzvamuse, Chandrasekhar Venkataraman
We present and analyse an implicit-explicit timestepping procedure with finite element spatial approximation for a semilinear reaction-diffusion systems on evolving domains arising…
A finite element method for fully nonlinear elliptic problems
Omar Lakkis, Tristan Pryer
We present a continuous finite element method for some examples of fully nonlinear elliptic equation. A key tool is the discretisation proposed in Lakkis & Pryer (2011, SISC) allow…
Global existence for semilinear reaction-diffusion systems on evolving domains
Chandrasekhar Venkataraman, Omar Lakkis, Anotida Madzvamuse
We present global existence results for solutions of reaction-diffusion systems on evolving domains. Global existence results for a class of reaction-diffusion systems on fixed dom…
A posteriori -error bounds in finite element approximation of the wave equation
Emmanuil H. Georgoulis, Omar Lakkis, Charalambos Makridakis
We address the error control of Galerkin discretization (in space) of linear second order hyperbolic problems. More specifically, we derive a posteriori error bounds in the L\infty…
A finite element method for second order nonvariational elliptic problems
Omar Lakkis, Tristan Pryer
We propose a numerical method to approximate the solution of second order elliptic problems in nonvariational form. The method is of Galerkin type using conforming finite elements…
Rate of convergence for a Galerkin scheme approximating a two-scale reaction-diffusion system with nonlinear transmission condition
Adrian Muntean, Omar Lakkis
We study a two-scale reaction-diffusion system with nonlinear reaction terms and a nonlinear transmission condition (remotely ressembling Henry's law) posed at air-liquid interface…
Gradient recovery in adaptive finite element methods for parabolic problems
Omar Lakkis, Tristan Pryer
We derive energy-norm aposteriori error bounds, using gradient recovery (ZZ) estimators to control the spatial error, for fully discrete schemes for the linear heat equation. This…
A posteriori error control for discontinuous Galerkin methods for parabolic problems
Emmanuil H. Georgoulis, Omar Lakkis, Juha M. Virtanen
We derive energy-norm a posteriori error bounds for an Euler time-stepping method combined with various spatial discontinuous Galerkin schemes for linear parabolic problems. For ac…
A posteriori error estimates in the maximum norm for parabolic problems
Alan Demlow, Omar Lakkis, Charalambos Makridakis
We derive a posteriori error estimates in the norm for approximations of solutions to linear para bolic equations. Using the elliptic reconstruction t…
A comparison of duality and energy aposteriori estimates for L?(0,T;L2(Ω)) in parabolic problems
Omar Lakkis, Charalambos Makridakis, Tristan Pryer
We use the elliptic reconstruction technique in combination with a duality approach to prove aposteriori error estimates for fully discrete back- ward Euler scheme for linear parab…