Search results for "Galerkin scheme"

showing 3 items of 3 documents

Adaptive discontinuous evolution Galerkin method for dry atmospheric flow

2014

We present a new adaptive genuinely multidimensional method within the framework of the discontinuous Galerkin method. The discontinuous evolution Galerkin (DEG) method couples a discontinuous Galerkin formulation with approximate evolution operators. The latter are constructed using the bicharacteristics of multidimensional hyperbolic systems, such that all of the infinitely many directions of wave propagation are considered explicitly. In order to take into account multiscale phenomena that typically appear in atmospheric flows nonlinear fluxes are split into a linear part governing the acoustic and gravitational waves and a nonlinear part that models advection. Time integration is realiz…

Backward differentiation formulasteady statesPhysics and Astronomy (miscellaneous)Wave propagationdry atmospheric convectionlarge time stepsystems of hyperbolic balance lawssymbols.namesakeDiscontinuous Galerkin methodApplied mathematicsevolution Galerkin schemesGalerkin methodMathematicssemi-implicit approximationNumerical AnalysisAdaptive mesh refinementApplied MathematicsEuler equationsRiemann solverComputer Science ApplicationsEuler equationsComputational MathematicsNonlinear systemClassical mechanicsModeling and SimulationsymbolsJournal of Computational Physics
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On a global superconvergence of the gradient of linear triangular elements

1987

Abstract We study a simple superconvergent scheme which recovers the gradient when solving a second-order elliptic problem in the plane by the usual linear elements. The recovered gradient globally approximates the true gradient even by one order of accuracy higher in the L 2 -norm than the piecewise constant gradient of the Ritz—Galerkin solution. A superconvergent approximation to the boundary flux is presented as well.

Applied MathematicsMathematical analysisOrder of accuracySuperconvergenceglobal superconvergence for the gradientComputer Science::Numerical AnalysisGlobal superconvergence for the gradientMathematics::Numerical AnalysisNonlinear conjugate gradient methodElliptic curveComputational Mathematicserror estimatesNorm (mathematics)boundary fluxPiecewisepost-processing of the Ritz—Galerkin schemeGradient descentGradient methodMathematicsJournal of Computational and Applied Mathematics
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Simulation of the Propagation of Tsunamis in Coastal Regions by a Two-Dimensional Non-Hydrostatic Shallow Water Solver

2017

Due to the enormous damages and losses of human lives in the inundated regions, the simulation of the propagation of tsunamis in coastal areas has received an increasing interest of the researchers. We present a 2D depth-integrated, non- hydrostatic shallow waters solver to simulate the propagation of tsunamis, solitary waves and surges in coastal regions. We write the governing continuity and momentum equations in conservative form and discretize the domain with unstructured triangular Generalized Delaunay meshes. We apply a fractional- time-step procedure, where two problems (steps) are consecutively solved. In the first and in the second step, we hypothesize a hydrostatic and a non-hydro…

TurbulenceVoronoi cellShallow waters; Non-hydrostatic pressure; Unstructured mesh; Wetting/drying; Tsunami propagation; Long waves; Voronoi cells; Runge-Kutta method; Galerkin scheme; Manning equation; Dirichlet condition; OpenFOAMShallow waterLong waveUnstructured meshGeophysicsSolverTsunami propagationSettore ICAR/01 - IdraulicaThermal hydraulicsWetting/dryingWaves and shallow waterBoundary layerNon-hydrostatic pressureDirichlet conditionFluid dynamicsRunge-Kutta methodOpenFOAMMagnetohydrodynamicsNavier–Stokes equationsGalerkin schemeGeologyManning equation
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