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→Numerical solutions
== Numerical solutions ==
== Numerical solutions ==
数值解
The three most widely used [[Numerical partial differential equations|numerical methods to solve PDEs]] are the [[finite element analysis|finite element method]] (FEM), [[finite volume method]]s (FVM) and [[finite difference method]]s (FDM), as well other kind of methods called [[Meshfree methods]], which were made to solve problems where the before mentioned methods are limited. The FEM has a prominent position among these methods and especially its exceptionally efficient higher-order version [[hp-FEM]]. Other hybrid versions of FEM and Meshfree methods include the generalized finite element method (GFEM), [[extended finite element method]] (XFEM), [[Spectral element method|spectral finite element method]] (SFEM), [[Meshfree methods|meshfree finite element method]], [[Discontinuous Galerkin Method|discontinuous Galerkin finite element method]] (DGFEM), [[Element-Free Galerkin Method]] (EFGM), [[Interpolating Element-Free Galerkin Method]] (IEFGM), etc.
The three most widely used [[Numerical partial differential equations|numerical methods to solve PDEs]] are the [[finite element analysis|finite element method]] (FEM), [[finite volume method]]s (FVM) and [[finite difference method]]s (FDM), as well other kind of methods called [[Meshfree methods]], which were made to solve problems where the before mentioned methods are limited. The FEM has a prominent position among these methods and especially its exceptionally efficient higher-order version [[hp-FEM]]. Other hybrid versions of FEM and Meshfree methods include the generalized finite element method (GFEM), [[extended finite element method]] (XFEM), [[Spectral element method|spectral finite element method]] (SFEM), [[Meshfree methods|meshfree finite element method]], [[Discontinuous Galerkin Method|discontinuous Galerkin finite element method]] (DGFEM), [[Element-Free Galerkin Method]] (EFGM), [[Interpolating Element-Free Galerkin Method]] (IEFGM), etc.
The three most widely used numerical methods to solve PDEs are the finite element method (FEM), finite volume methods (FVM) and finite difference methods (FDM), as well other kind of methods called Meshfree methods, which were made to solve problems where the before mentioned methods are limited. The FEM has a prominent position among these methods and especially its exceptionally efficient higher-order version hp-FEM. Other hybrid versions of FEM and Meshfree methods include the generalized finite element method (GFEM), extended finite element method (XFEM), spectral finite element method (SFEM), meshfree finite element method, discontinuous Galerkin finite element method (DGFEM), Element-Free Galerkin Method (EFGM), Interpolating Element-Free Galerkin Method (IEFGM), etc.
The three most widely used numerical methods to solve PDEs are the finite element method (FEM), finite volume methods (FVM) and finite difference methods (FDM), as well other kind of methods called Meshfree methods, which were made to solve problems where the before mentioned methods are limited. The FEM has a prominent position among these methods and especially its exceptionally efficient higher-order version hp-FEM. Other hybrid versions of FEM and Meshfree methods include the generalized finite element method (GFEM), extended finite element method (XFEM), spectral finite element method (SFEM), meshfree finite element method, discontinuous Galerkin finite element method (DGFEM), Element-Free Galerkin Method (EFGM), Interpolating Element-Free Galerkin Method (IEFGM), etc.
求解偏微分方程最常用的三种数值方法是有限元分析法、有限体积法和差分法，以及其他一些称为无网格法的方法。这些方法用于解决前面提到的方法受到的限制。在这些方法中，有限元方法，尤其是高效的高阶有限元方法，占有重要地位。有限元法和无网格法的其他混合形式包括广义有限元分析法(GFEM)、扩展有限元分析法(XFEM)、谱有限元分析法(SFEM)、无网格有限元分析法(DGFEM)、间断有限有限元分析法(DGFEM)、无网格伽辽金法(EFGM)、插值无网格伽辽金法(IEFGM)等。
=== Finite element method ===
=== Finite element method ===
有限元方法
{{main|Finite element method}}
{{main|Finite element method}}
类似于有限差分法或有限元分析，数值是在网状几何体的离散位置计算的。“有限体积”是指网格上每个节点周围的小体积。在有限体积法中，含有散度项的偏微分方程中的表面积分用高斯散度定理积分转换成体积分。然后将这些项计算为每个有限体积表面的通量。由于进入给定体积的磁通量与离开相邻体积的磁通量相同，这些方法在设计上保持了质量。
类似于有限差分法或有限元分析，数值是在网状几何体的离散位置计算的。“有限体积”是指网格上每个节点周围的小体积。在有限体积法中，含有散度项的偏微分方程中的表面积分用高斯散度定理积分转换成体积分。然后将这些项计算为每个有限体积表面的通量。由于进入给定体积的磁通量与离开相邻体积的磁通量相同，这些方法在设计上保持了质量。
==See also==
==See also==