Mathematics of Computation · 1994 · 206 citations · 23 references
ComputingComputational EngineeringComputational Fluid DynamicsFinite Element MethodsFluid DynamicsConvergence AnalysisEigenvalue ProblemsError EstimationFinite Element DiscretizationNonlinear Finite Element AnalysisNumerical AnalysisA Posteriori Error EstimatesA Posteriori Error EstimationElliptic Partial Differential EquationsError Estimation For Eigenvalue ProblemsError Estimation For Finite Element SolutionsFinite-dimensional ApproximationIncompressible Navier-stokes EquationsLower Bounds
Abstract. Using the abstract framework of [9] we analyze a residual a posteriori error estimator for space-time finite element discretizations of quasilinear parabolic pdes. The estimator gives global upper and local lower bounds on the error of the numerical solution. The finite element discretizations in particular cover the so-called θ-scheme, which includes the implicit and explicit Euler methods and the Crank-Nicholson scheme. 1.
23