Explicit Time Stepping for the Wave Equation using CutFEM with Discrete Extension
Erik Burman, Peter Hansbo, Mats G. Larson
Abstract
In this paper we develop a fully explicit cut finite element method for the wave equation. The method is based on using a standard leap frog scheme combined with an extension operator that defines the nodal values outside of the domain in terms of the nodal values inside the domain. We show that the mass matrix associated with the extended finite element space can be lumped leading to a fully explicit scheme. We derive stability estimates for the method and provide optimal order a priori error estimates. Finally, we present some illustrating numerical examples.
Topics & Concepts
MathematicsExtension (predicate logic)A priori and a posterioriFinite element methodWave equationDomain (mathematical analysis)Applied mathematicsStability (learning theory)Matrix (chemical analysis)Operator (biology)Mathematical analysisComputer scienceGeneChemistryRepressorComposite materialMachine learningEpistemologyTranscription factorThermodynamicsBiochemistryMaterials sciencePhilosophyPhysicsProgramming languageAdvanced Numerical Methods in Computational MathematicsElectromagnetic Simulation and Numerical MethodsNumerical methods for differential equations