This paper presents an output-based error estimation and adaptation strategy for hybridized discontinuous Galerkin discretizations of firstand second-order systems of conservation laws. A discrete adjoint solution is obtained by a Schurcomplement solver similar to that used in the primal problem. An error estimate is obtained by computing the adjoint on an enriched solution space that consists ...

We generalize the a posteriori techniques for the linear heat equation in [Ver03] to the case of the nonlinear parabolic p-Laplace problem thereby proving reliable and efficient a posteriori error estimates for a fully discrete implicite Euler Galerkin finite element scheme. The error is analyzed using the so-called quasi-norm and a related dual error expression. This leads to equivalence of th...

For the Fredholm integral equation u=T u+f on the real line, fast solvers are designed on the basis of a discretized wavelet Galerkin method with the Sloan improvement of the Galerkin solution. The Galerkin system is solved by GMRES or by the Gauss elimination method. Our concept of the fast solver includes the requirements that the parameters of the approximate solution un can be determined in...

We consider a discontinuous Galerkin finite element method for the advection–reaction equation in two space–dimensions. For polynomial approximation spaces of degree greater than or equal to two on triangles we propose a method where stability is obtained by a penalization of only the upper portion of the polynomial spectrum of the jump of the solution over element edges. We prove stability in ...

We study a posteriori error estimates for the numerical approximations of state constrained optimal control problems governed by convection diffusion equations, regularized by Moreau-Yosida and Lavrentiev-based techniques. The upwind Symmetric Interior Penalty Galerkin (SIPG) method is used as a discontinuous Galerkin (DG) discretization method. We derive different residual-based error indicato...

A weighted essential non-oscillatory reconstruction scheme based on Hermite polynomials is developed and applied as a limiter for a discontinuous Galerkin finite element method on unstructured grids. The solution polynomials are reconstructed using a WENO scheme by taking advantage of handily available and yet valuable information, namely the derivatives, in the context of the discontinuous Gal...

The aim of this paper is to find the numerical solutions of the second order linear and nonlinear differential equations with Dirichlet, Neumann and Robin boundary conditions. We use the Bernoulli polynomials as linear combination to the approximate solutions of 2nd order boundary value problems. Here the Bernoulli polynomials over the interval [0, 1] are chosen as trial functions so that care ...

In this work, numerical and experimental analyses of a double-pipe heat exchanger with SiO2 nanoparticles were performed. The study was conducted by using the k-e turbulence model Galerkin weighted residual finite element method. nanofluid used in inner pipe at various solid particle volume fractions. Effects flow rate temperature on overall transfer coefficient examined. Brownian motion effect...

This paper considers the numerical solution of time-dependent convection-diffusion-reaction equations. We shall employ combinations of streamlineupwind Petrov–Galerkin (SUPG) and local projection stabilization (LPS) meth-ods in space with the higher order variational time discretization schemes. In particular, we consider time discretizations by discontinuous Galerkin (dG) meth-ods and continuo...