HighWire Press Open Archive · 56 citations · 21 references
ComputingMechanical EngineeringPhysicsComputational Fluid DynamicsFinite Element MethodsFluid DynamicsCompressible FlowConvergence AnalysisError EstimationFinite Element DiscretizationNavier-stokes EquationsNumerical ConvergenceA Posteriori Error EstimatesApproximation ErrorCompressible Navier-stokes EquationsDiscretizationDiscretization Error AnalysisError Estimation For Finite Element SolutionsError Estimation For Time-dependent ProblemsSpace-time Discretization
We present here a general method based on the investigation of the relative energy of the system that provides an unconditional error estimate for the approximate solution of the barotropic Navier–Stokes equations obtained by time and space discretization. We use this methodology to derive an error estimate for a specific DG/finite element scheme for which the convergence was proved in Karper (2013, <it>Numer. Math.</it>, <b>125</b>, 441–510).
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