We identify and study an LDG-hybridizable Galerkin method, which is not LDG for second-order elliptic problems in several space dimensions with remarkable convergence properties. Unlike all other known discontinuous methods using polynomials of degree $k\ge 0$ both the potential as well flux, order $L^2$ unknowns $k+1$. Moreover, approximate its numerical trace superconverge $L^2$-like norms, to suitably chosen projections potential, $k+2$. This allows application element-by-element...

In this article, we propose a novel discontinuous Galerkin method for convection-diffusion-reaction problems, characterized by three main properties. The first is that the hybridizable; renders it efficiently implementable and competitive with existing methods these problems. second that, when uses polynomial approximations of same degree both total flux scalar variable, optimal convergence properties are obtained variables; in sharp contrast all other problem. third exhibits...

We analyze a local discontinuous Galerkin method for fourth-order time-dependent problems. Optimal error estimates are obtained in one dimension and multidimensions Cartesian triangular meshes. extend the analysis to higher even-order equations linearized Cahn–Hilliard type equations. Numerical experiments displayed verify theoretical results.

We show that the approximation given by original discontinuous Galerkin method for transport-reaction equation in d space dimensions is optimal provided meshes are suitably chosen: $L^2$-norm of error order $k+1$ when uses polynomials degree k. These not necessarily conforming and do satisfy any uniformity condition; they required only to be made simplexes, each which has a unique outflow face. also find new, element-by-element postprocessing derivative direction flow superconverges with $k+1$.

We prove optimal convergence rates for the approximation provided by original discontinuous Galerkin method transport-reaction problem. This is achieved in any dimension on meshes related a suitable way to possibly variable velocity carrying out transport. Thus, if uses polynomials of degree k, $L^2$-norm error order $k+1$. Moreover, we also show that, means an element-by-element postprocessing, new approximate flux can be obtained which superconverges with

We design and analyze <italic>the first</italic> hybridizable discontinuous Galerkin methods for stationary, third-order linear equations in one-space dimension. The are defined as discrete versions of characterizations the exact solution terms local problems transmission conditions. They provide approximations to <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="u"> <mml:semantics> <mml:mi>u</mml:mi> <mml:annotation...

Journal Article A new discontinuous Galerkin method, conserving the discrete H2 -norm, for third-order linear equations in one space dimension Get access Yanlai Chen, Chen Department of Mathematics, University Massachusetts Dartmouth, 285 Old Westport Road, North MA 02747, USAyanlai.chen@umassd.edu Search other works by this author on: Oxford Academic Google Scholar Bernardo Cockburn, Cockburn School Minnesota, Minneapolis, MN 55455, USAcockburn@math.umn.edu Bo Dong * USA *Corresponding...

During geomagnetic disturbances, the telluric currents which are driven by induced electric fields will flow in conductive Earth. An approach to model Earth conductivity structures with lateral changes for calculating geoelectric is presented this paper. Numerical results, obtained Finite Element Method (FEM) a planar grid two-dimensional modelling and solid three-dimensional modelling, compared, of different regions demonstrated. Then structure modelled depths field at Earth’s surface...

Mixed trigonometric polynomial systems arise in many fields of science and engineering. Commonly, this class is transformed into by variable substituting adding some quadratic equations, then solved system solving method. In paper, exploiting the special structure additional an efficient hybrid method for coming from mixed presented. It combines homotopy method, which a combination coefficient parameter random product homotopy, with decomposition, substitution, reduction techniques....

Abstract The induced geoelectric fields and telluric currents generated during geomagnetic storms will be distorted by lateral variations of the Earth conductivity. Galerkin finite element method (FEM) is a useful tool to analyze complicated electromagnetic field problems. In this paper, uniform thin sheet current with infinite width located at 100 km above Earth's surface assumed represent source variations. It harmonic amplitude 1 A/m different frequencies. Three conductivity structures...

.We design, analyze, and implement a new conservative discontinuous Galerkin (DG) method for the simulation of solitary wave solutions to generalized Korteweg–de Vries (KdV) equation. The key feature our is conservation, at numerical level, mass, energy, Hamiltonian that are conserved by exact all KdV equations. To knowledge, this first DG conserves these three quantities, property critical accurate long-time evolution waves. achieve desired conservation properties, novel idea introduce two...

Many natural phenomena can be modeled by a second-order dynamical system , where stands for an appropriate state variable and M, C, K are time-invariant, real symmetric matrices. In contrast to the classical inverse vibration problem model is determined from frequencies corresponding various boundary conditions, mode concerns reconstruction of coefficient matrices (M, K) prescribed or observed subset modes. This paper set forth mathematical framework resolves some open questions raised in...

We develop and analyze the first hybridizable discontinuous Galerkin (HDG) method for solving fifth-order Korteweg-de Vries (KdV) type equations. show that semi-discrete scheme is stable with proper choices of stabilization functions in numerical traces. For linearized equations, we prove approximations to exact solution its four spatial derivatives as well time derivative all have optimal convergence rates. The experiments, demonstrating rates both linear nonlinear validate our theoretical findings.

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We develop and analyze a new hybridizable discontinuous Galerkin (HDG) method for solving third-order Korteweg-de Vries type equations. The approximate solutions are defined by discrete version of characterization the exact solution in terms to local problems on each element which patched together through transmission conditions interfaces. prove that semi-discrete scheme is stable with proper choices stabilization function numerical traces. For linearized equation, we carry out error...