Intersecting into inner corners of walls, when walking into them.

Hi,

I have a capsule as a player and a mesh collider as a level... The creases in faces on the level mainly consist of right angles. When I walk into an inner corner of the room, my character intersects? I have no idea what is going on, and I really could use some assistance. I used this bit of code to move my character, and my fixed framerate is 100FPS.

 using UnityEngine;
 using System.Collections;
 
 public class PlayerController : MonoBehaviour {
 
     public float speed;
     private float mouseX;
     private float mouseY;
     public float xSensitiv;
     public float ySensitiv;
     public float jumpForce;
 
     void FixedUpdate () {
         if (Input.GetKey (KeyCode.W))
         {
             GetComponent <Rigidbody> ().position += transform.forward * speed * Time.deltaTime;
         }
         if (Input.GetKey (KeyCode.A))
         {
             GetComponent <Rigidbody> ().position -= transform.right * speed * Time.deltaTime;
         }
         if (Input.GetKey (KeyCode.S))
         {
             GetComponent <Rigidbody> ().position -= transform.forward * speed * Time.deltaTime;
         }
         if (Input.GetKey (KeyCode.D))
         {
             GetComponent <Rigidbody> ().position += transform.right * speed * Time.deltaTime;
         }
         mouseX += Input.GetAxis ("Mouse X") * xSensitiv * Time.deltaTime;
         GetComponent <Rigidbody> ().rotation = Quaternion.Euler (0, mouseX, 0);
         mouseY -= Input.GetAxis ("Mouse Y") * ySensitiv * Time.deltaTime;
         mouseY = Mathf.Clamp (mouseY, -90, 90);
         Camera.main.transform.localRotation = Quaternion.Euler (mouseY, 0, 0);
         if (Input.GetKey (KeyCode.Space) && Physics.Raycast (transform.position + Vector3.down * 0.875f, Vector3.down, 0.25f))
         {
             GetComponent <Rigidbody> ().velocity += Vector3.up * jumpForce;
         }
     }
 }