A weak Galerkin finite element method for parabolic singularly perturbed convection-diffusion equations on layer-adapted meshes
Şuayip Toprakseven, Seza Dinibütün
Abstract
<p>In this paper, we designed and analyzed a weak Galerkin finite element method on layer adapted meshes for solving the time-dependent convection-dominated problems. Error estimates for semi-discrete and fully-discrete schemes were presented, and the optimal order of uniform convergence has been obtained. A special interpolation was delicately designed based on the structures of the designed method and layer-adapted meshes. We provided various numerical examples to confirm the theoretical findings.</p>
Topics & Concepts
Galerkin methodPolygon meshFinite element methodConvection–diffusion equationConvectionDiscontinuous Galerkin methodDiffusionMathematicsMathematical analysisLayer (electronics)Parabolic partial differential equationMechanicsMaterials sciencePhysicsGeometryPartial differential equationThermodynamicsComposite materialDifferential Equations and Numerical MethodsAdvanced Numerical Methods in Computational MathematicsAdvanced Mathematical Modeling in Engineering