This paper presents a Streamline-Upwind Petrov–Galerkin (SUPG) reduced order model (ROM) based on Proper Orthogonal Decomposition (POD). This ROM is investigated theoretically and numerically for convection-dominated convectiondi usion-reaction equations. The SUPG finite element method was used on realistic meshes for computing the snapshots, leading to some noise in the POD data. Numerical ana...

We develop a family of Eulerian-Lagrangian localized adjoint methods for the solution of the initial-boundary value problems for rst-order advection-reaction equations on general multi-dimensional domains. Diierent tracking algorithms, including the Euler and Runge-Kutta algorithms, are used. The derived schemes naturally incorporate innow boundary conditions into their formulations and do not ...

This paper studies the discontinuous Petrov–Galerkin (DPG) method, where the test space is normed by a modified graph norm. The modification scales one of the terms in the graph norm by an arbitrary positive scaling parameter. The main finding is that as the parameter approaches zero, better results are obtained, under some circumstances, when the method is applied to the Helmholtz equation. Th...

We discuss numerical properties of continuous Galerkin-Petrov and discontinuous Galerkin time discretizations applied to the heat equation as a prototypical example for scalar parabolic partial differential equations. For the space discretization, we use biquadratic quadrilateral finite elements on general two-dimensional meshes. We discuss implementation aspects of the time discretization as w...

The Discontinuous Petrov–Galerkin (DPG) method is a widely employed discretization for Partial Differential Equations (PDEs). In recent work, we applied the DPG with optimal test functions time integration of transient parabolic PDEs. We showed that resulting DPG-based time-marching scheme equivalent to exponential integrators trace variables. this extend aforementioned time-dependent hyperboli...

In this note, we extend our recent work for the heat equation in [1] and compare numerically continuous Galerkin-Petrov (cGP) and discontinuous Galerkin (dG) time discretizations for the nonstationary Stokes equations in two dimensions. For the space discretization, we use the LBB-stable finite element pair Q2/P disc 1 and we discuss implementation aspects as well as methods for solving the res...

In this work we compare semi-discrete formulations to obtain numerical solutions for the 1D Burgers equation. The formulations consist in the discretization of the time-domain via multi-stage methods of second and fourth order: R11 and R22 Padé approximants, and of the spatial-domain via finite element methods: least-squares (MEFMQ), Galerkin (MEFG) and Streamline-Upwind Petrov-Galerkin (SUPG)....

We propose and study numerically the implicit approximation in time of Navier–Stokes equations by a Galerkin–collocation method combined with inf–sup stable finite element methods space. The conceptual basis approach is establishment direct connection between Galerkin classical collocation methods, perspective achieving accuracy former reduced computational costs terms less complex algebraic sy...

Abstract In this paper, we propose a certified reduced basis (RB) method for quasilinear parabolic problems with strongly monotone spatial differential operator. We provide residual-based posteriori error estimate space-time formulation and the corresponding efficiently computable bound certification of method. introduce Petrov-Galerkin finite element discretization continuous problem use it as...