An oscillation free local discontinuous Galerkin method for nonlinear degenerate parabolic equations
Qi Tao, Yong Liu, Yan Jiang, Jianfang Lu
Abstract
Abstract An oscillation free local discontinuous Galerkin (OFLDG) method is proposed for solving nonlinear degenerate parabolic equations. The damping terms are added to the original LDG scheme to control the spurious oscillations when solutions have a large gradient. The L 2 ‐stability and optimal priori error estimates for the semi‐discrete scheme in one‐ and multi‐dimensions are established. The numerical experiments demonstrate that the proposed method maintains the high order accuracy and controls the spurious oscillations well.
Topics & Concepts
Degenerate energy levelsMathematicsSpurious relationshipNonlinear systemOscillation (cell signaling)Galerkin methodDiscontinuous Galerkin methodA priori and a posterioriMathematical analysisStability (learning theory)Scheme (mathematics)Applied mathematicsFinite element methodPhysicsComputer scienceMachine learningQuantum mechanicsGeneticsPhilosophyBiologyStatisticsEpistemologyThermodynamicsAdvanced Numerical Methods in Computational MathematicsComputational Fluid Dynamics and AerodynamicsDifferential Equations and Numerical Methods