Stabilizer-free weak Galerkin methods for monotone quasilinear elliptic PDEs
Xiu Ye, Shangyou Zhang, Yunrong Zhu
Abstract
In this paper, we study the stabilizer-free weak Galerkin methods on polytopal meshes for a class of second order elliptic boundary value problems of divergence form and with gradient nonlinearity in the principal coefficient. With certain assumptions on the nonlinear coefficient, we show that the discrete problem has a unique solution. This is achieved by showing that the associated operator satisfies certain continuity and monotonicity properties. With the help of these properties, we derive optimal error estimates in the energy norm. We present several numerical examples to verify the error estimates.
Topics & Concepts
MathematicsGalerkin methodMonotone polygonNonlinear systemApplied mathematicsMonotonic functionNorm (philosophy)Polygon meshDiscontinuous Galerkin methodBoundary value problemMathematical analysisElliptic operatorDivergence (linguistics)Operator (biology)Finite element methodGeometryPhysicsLawQuantum mechanicsGeneBiochemistryLinguisticsPolitical scienceRepressorTranscription factorThermodynamicsChemistryPhilosophyAdvanced Numerical Methods in Computational MathematicsAdvanced Mathematical Modeling in EngineeringDifferential Equations and Numerical Methods